# Time, Speed, Distance, Train and Boat Problems

#### Question No 1

A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?

Solution!
Rate downstream = (16/2)km/h = 8 km/h! !Rate upstream = (16/4)km/h!= 4 km/h! !Hence, Speed in still water = 1/2(8+4)km/h = 6 km/h.

#### Question No 2

230 meters long train crosses a man sitting on the platform in 46 seconds. What is the speed of the train?

Solution!
Length of the train = L = 230m!Time = t = 46s!Speed = v = ?! !V = L/t!By putting values!v = 230/46 = 5m/s! !Hence speed of the train is 5m/s..

#### Question No 3

A boat travels at the speed of 25 km/h upstream and 35 km/h downstream. Find the speed of water.

Solution!
Upstream speed = y = 25 Km/h!Downstream speed = x = 35 Km/h!Speed of water = (1/2)*(x-y)!= (1/2)*(35-35) = 5 Km/h.

#### Question No 4

What is the length of a bridge if a train of length 550 meters travelling at the speed of 20m/s can cross it in 35 seconds?

Solution!
Length of train = L1 = 550m!Speed = v = 20m/s!Time = t = 35s!Length of bridge = L2 = ?! !t = (L1+L2)/v!By putting values!35 = (550+L2)/20!700 - 550 = L2!L2 = 150m! !Hence length of bridge is 150 meter..

#### Question No 5

Joseph's speed of rowing in still water is 12 km/h and he finds that it takes him twice as long to row up as to row down the river. Find the speed of water in the river.

Solution!
Let speed of water is x.!Speed in still water = u = 12 Km/h! !As downstream speed is double of upstream speed! !(12+x) = 2(12-x)!12+x = 24-2x!3x = 12!x = 4! !Hence speed of water is 4 Km/h..

#### Question No 6

A train is running at a speed of 10 km/h. What will be the distance covered by it in 3 hours?

Solution!
As we know that!S=vt (here S is distance, v is speed and t is time). So!distance = 10*3 = 30Km.

#### Question No 7

A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?

Solution!
Speed downstream = (5 + 1) kmph = 6 kmph! !Speed upstream = (5 - 1) kmph = 4 kmph! !Let the required distance be x km.! !Then,! x/6 + x/4 = 1!2x + 3x = 12!5x = 12! !Hence, x = 2.4 km.

#### Question No 8

A man rowing a boat covers an average distance of 7.5 km/h. What is the distance covered after 40 minutes?

Solution!
Distance covered in 60 minutes = 7.5 Km!Distance covered in 1 minute = 7.5/60 = 1/8 Km! !Distance covered in 40 minutes = (1/8)*40 = 5 Km.

#### Question No 9

A train 100 meters long crosses a 150 meters long bridge in 25 seconds. What is the speed of the train?

Solution!
Length of the train = L1 = 100m!Length of the bridge = L2 = 150m!Time = t = 25s! !v = (L1+L2)/t!By putting values!v = (100+150)/25!v = 250/25 = 10m/s = 10*(18/5) = 36 Km/h! !Hence speed of the train is 36 Km/h..

#### Question No 10

A train travelling at 36 km/h took 10 seconds to pass a stationary man. What was the length of the train?

Solution!
Speed = v = 36 Km/h = 36*(5/18) = 10m/s!Time = t = 10s!Length of the train = L = ?! !L = v*t!By putting values!L = 10*10 = 100m! !Hence length of the train is 100 meter..

#### Question No 11

Ali's swimming speed in still water is 18 km/h and speed of water is 6 km/h. How long will it take him to go downstream 72km?

Solution!
Ali's swimming speed in still water = u = 18 Km/h!Speed of water = v = 6 Km/h!Total speed down the stream = 18+6 = 24 Km/h! !Distance to cover = 72 Km!time = ?! !time = distance/speed = time = 72/24 = 3 hours..

#### Question No 12

A man rows 1 km upstream in 20 minutes and 1 km downstream in 15 minutes. What is his speed of rowing in still water?

Solution!
20 minutes = 20/60 = 1/3 hours!Upstream distance covered in 1/3 hours = 1 Km!Upstream distance covered in 1 hour = 1/(1/3) = 3 Km!Upstream speed = y = 3 Km/h! !Now!15 minutes = 15/60 = 1/4 hours!Downstream distance covered in 1/4 hours = 1 Km!Downstream distance covered in 1 hour = 1/(1/4) = 4 Km!Downstream speed = 4 Km/h! !speed of rowing = (1/2)*(4+3) = 7/2 = 3.5 Km/h.

#### Question No 13

A train travelling at the speed of 10m/s can cross a bridge in 23 seconds. If length of the train is 120 meters. What is length of the bridge?

Solution!
Speed = v = 10m/s!Time = t = 23s!Length of train = L1 = 120m!Length of bridge = L2 = ?! !t = (L1+L2)/v!By putting values!23 = (120+L2)/10!L2 = 230 - 120 = 110m! !Hence bridge is 110m long..

#### Question No 14

A train is running at the speed of 70 km/h. How far will it travel in 2.5 hrs?

Solution!
Speed = v = 70 Km/h!Time = t = 2.5h!Distance = S = v*t = 70*2.5 = 175Km.

#### Question No 15

Two trains are moving in opposite directions at speed of 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train is

Solution!
Relative speed = (60+ 90) km/hr!= 150 * (5/18)m/s!= (125/3)m/s! !Distance covered = (1.10 + 0.9) km = 2 km = 2000 m! !Hence, Required time = 2000(3/125) = 48 seconds.

#### Question No 16

A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.

Solution!
Speed downstream = (13 + 4) km/hr = 17 km/hr! !Time taken to travel 68 km downstream = (68/17)hrs!= 4 hours.

#### Question No 17

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is

Solution!
Speed of the train relative to man = (125/10) m/s!= (25/2)m/s!= (25/2) * (18/5)km/hr!= 45 km/hr! !Let the speed of the train be x km/hr.!Then,!relative speed = (x - 5) km/hr! !x - 5 = 45!Hence, x = 50 km/hr.

#### Question No 18

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

Solution!
Speed = 54 * (5/18)m/s!= 15 m/s! !Length of the train = (15 x 20)m = 300 m! !Let the length of the platform be x metres! !Then,!(x+300)/36 = 15!x + 300 = 540! !Hence, x = 240 m.

#### Question No 19

Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train is

Solution!
Let the speed of each train be x m/sec.! !Then, relative speed of the two trains = 2x m/sec.! !So, 2x = (120 + 120)/12!2x = 20!x = 10! !Hence, Speed of each train = 10 m/sec = 10 * (18/5)!= 36 km/hr.

#### Question No 20

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is

Solution!
2 kmph = 2 * (5/18)m/s!= 5/9 m/s! !4 kmph = 4 * (5/18)m/s!= 10/9 m/s! !Let the length of the train be x metres and its speed by y m/sec.! !then, x/[y - (5/9)] = 9!and x/[y - (10/9)] = 10! !So, 9y - 5 = x!and 10(9y - 10) = 9x! !9y - x = 5!and 90y - 9x = 100! !On solving, we get! x = 50! !Hence, Length of the train is 50 m..

#### Question No 21

A man can row 4.5 km an hour in still water but takes twice as long to row up a stream as down it. What is the rate of stream in km/h?

Solution!
Let rate of stream (speed of water) is x.!Man's speed in still water = u = 4.5 Km/h! !Given that!4.5+x = 2(4.5-x)!4.5+x = 9-2x!3x = 4.5!x = 1.5! !Hence rate of stream is 1.5 Km/h.

#### Question No 22

John can swim at the speed of 20 km/h in still water and speed of water is 3 km/h. What is his swimming speed with water?

Solution!
John's speed in still water = u = 20 Km/h!Speed of water = v = 3 Km/h!John's speed with water = u+v = 20+3 = 23 Km/h.

#### Question No 23

If a man takes two hours to row 3 km upstream or 15 km downstream then the speed of current is?

Solution!
Upstream distance covered in 2 hours = 3Km!Distance covered in 1 hour = 3/2 = `1.5 Km!So,!Upstream speed = 1.5 Km/h!Downstream distance covered in 2 hours = 15Km!Distance covered in 1 hour = 15/2 = 7.5Km! !Downstream speed = 7.5 Km/h! !Now!Speed of water = (1/2)*(7.5-1.5) = 3 Km/h.

#### Question No 24

What is the speed of the train if it crosses a 175 meters long bridge in 41 seconds? Length of the train is 645 meters?

Solution!
Length of the train = L1 = 645m!Length of the bridge = L2 = 175m!Time = t = 41s!Speed = v = ?! !v = (L1+L2)/t!v = (645+175)/41!v = 20m/s = 20 * 18/5 = 72 Km/h! !Hence speed of the train is 72 Km/h..

#### Question No 25

A man can row down a 10 mile stream in 2 hours and up in 5 hours. What is the average speed in miles per hour?

Solution!
Downstream distance covered in 2 hours = 10 miles!Downstream distance covered in 1 hour = 10/2 = 5 miles!Downstream speed = 5 mile/h! !and!Upstream distance covered in 5 hours = 10 mile!Upstream distance covered in 1 hour = 10/5 = 2 miles! !Upstream speed = 2 mile/hr! !Average speed = (1/2)*(2+5) = 3.5 mile/hr.

#### Question No 26

A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is

Solution!
Let the speed of the stream be x km/hr.! !Then,!Speed downstream = (15 + x) km/hr! !Speed upstream = (15 - x) km/hr! !So, [30/(15 + x)] + [30/(15 - x)] = 9/2!900/(225 - x*x) = 9/2! !x = 5 km/hr.

#### Question No 27

Speed of water in certain river is 2 km/h and it takes a boat thrice as long to row up as to row down the river. Find the speed of the boat in still water.

Solution!
Let speed of boat in still water is x.!Speed of water = v = 2 Km/h! !As downstream speed in 3 times the upstream speed so!(x+2) = 3(x-2)!x+2 = 3x-6!8 = 2x!x = 4!Hence speed of boat in still water is 4 Km/h.

#### Question No 28

A 100 meters long train can cross a 150 meters long bridge in 20 seconds. What is the speed of the train?

Solution!
Length of the train = L1 = 100m!Length of the bridge = L2 = 150m!Time = t = 20s!Speed = v = ?! !v = (L1+L2)/t!By putting values!v = (100+150)/20!v = 250/20 = 12.5m/s! !Hence speed of train is 12.5m/s..

#### Question No 29

Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds.If one is moving twice as fast the other, then the speed of the faster train is

Solution!
Let the speed of the slower train be x m/sec! !Then,!speed of the faster train = 2x m/sec! !Relative speed = (x + 2x) m/sec = 3x m/sec! !So, (100+100)/8 = 3x!24x = 200!x = 25/3! !So, speed of the faster train = 50/3 m/s!= (50/3 * 18/5)!= 60km/hr.

#### Question No 30

The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is

Solution!
Speed downstream = (15 + 3) kmph = 18 kmph! !Distance travelled = 18 * (12/60)km = 3.6 km.

#### Question No 31

A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

Solution!
Formula for converting from km/hr to m/s is!X km/hr = x * (5/18)m/s! !Therefore,!Speed = 45 * (5/18) = 25/2 m/s! !Total distance to be covered = (360 + 140) m = 500 m! !Formula for finding Time = (Distance/Speed)! !Hence, Required time = (500*2)/25!= 40 seconds.

#### Question No 32

A train is running at the speed of 25 km/h. How far will it travel in 5 hrs?

Solution!
Speed = v = 25 Km/h!Time = t = 5h!Distance = S = v*t = 25*5 = 125Km.

#### Question No 33

In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is

Solution!
Speed in still water!= 1/2(11+5) km/h = 8 km/h.

#### Question No 34

A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

Solution!
Speed = 72 * (5/18)m/s!= 20 m/s! !Time = 26 sec! !Let,!the length of the train be x metres! !Then,!(x+250)/26 = 20! !x + 250 = 520!x = 270.

#### Question No 35

A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is

Solution!
Speed = 78 * (5/18) = 65/3 m/s! !Time = 1 minute = 60 seconds! !Let the length of the tunnel be x metres! !Then,!(800+x)/60 = 65/3!3(800 + x) = 3900! !Hence, x = 500.

#### Question No 36

Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is

Solution!
Let the length of each train be x metres.! !Then, distance covered = 2x metres.! !Relative speed = (46 - 36) km/hr!= 10 * (5/18)m/s!= 25/9 m/s!So, 2x/36 = 25/9!= 2x = 100! !Hence, x = 50.

#### Question No 37

A train is travelling at the speed of 25m/s. In what time will it pass a man sitting on a platform if length of the train is 225 meters?

Solution!
Speed = v = 25m/s!Length of train = L = 225m! !Time = t = L/v!t = 225/25 = 9! !Hence train will pass the man in 9 seconds..

#### Question No 38

A train running at the speed of 60 km/hr crosses a pole in 9 seconds.What is the length of the train?

Solution!
Speed = 60 * (5/18) = 50/3 m/sec! !Length of the train = (Speed x Time) = (50/3) * 9 = 150 meters.

#### Question No 39

Anil's swimming speed in still water is 14 km/h and speed of water is 4 km/h. How long will it take him to go upstream 50 km?

Solution!
Anil's swimming speed in still water = u = 14 Km/h!Speed of water = v = 4 Km/h!Total upstream speed = u-v = 14-10 = 10 Km/h!Distance to cover = S = 50Km! !time = distance/speed!By putting values!time = t = 50/10 = 5 hours.

#### Question No 40

A man can row 1 km upstream in 20 minutes, and downstream in 15 minutes. What is the speed of the current?

Solution!
20 minutes = 20/60 = 1/3 hours!Upstream distance covered in 1/3 hours = 1 Km!Upstream distance covered in 1 hour = 1/(1/3) = 3 Km!Upstream speed = y = 3 Km/h! !Now!15 minutes = 15/60 = 1/4 hours!Downstream distance covered in 1/4 hours = 1 Km!Downstream distance covered in 1 hour = 1/(1/4) = 4 Km!Downstream speed = 4 Km/h! !speed of water = (1/2)*(4-3) = 1/2 = 0.5 Km/h.

#### Question No 41

How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

Solution!
Speed of the train relative to man = (63 - 3) km/hr!= 60 km/hr = 60 * (5/18)m/s!= (50/3)m/s! !Hence, Time taken to pass the man!= 500 * (3/50)s!= 30 seconds.

#### Question No 42

A train of length 150 metres is running at the speed of 20m/s. In what time will it cross a 130 metre long bridge?

Solution!
Length of the train = L1 = 150m!Length of bridge = L2 = 130m!Speed = v = 20m/s! !t = (L1 + L2)/v!t = (150+130)/20!t = 14! !Hence the train will pass the 130 meter long bridge in 14 seconds..

#### Question No 43

A 150m long train is running at the speed of 36km/h. In what time will it pass the 80m long bridge?

Solution!
Length of train = L1 = 150m!Speed = v = 36 Km/h = 36*(5/18) = 10 m/s!Length of bridge = L2 = 80m! !Time = t = (L1 + L2)/v!t = (150+80)/10 = 23! !Hence the train will pass the 80 meter long bridge in 23 seconds..

#### Question No 44

A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

Solution!
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.!= 66 * (5/18) = (55/3)m/s! !Hence, Time taken to pass the man!= 110 * (3/55) = 6 seconds.

#### Question No 45

A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds.What is the length of the platform?

Solution!
Speed = (300/18)m/s!= 50/3m/s! !Let the length of the platform be x metres! !Then, (x+300)/39 = 50/3!3(x + 300) = 1950! !Hence, x = 350 m.

#### Question No 46

Speed of water in certain river is 6 km/h and it takes a boat four times as long to row up as to row down the river. What is the speed of boat in still water?

Solution!
Let speed of boat in still water is x.!Speed of water = v = 6 Km/h!As downstream speed is four times the upstream speed so! !(x+6) = 4(x-6)!x+6 = 4x-24!30 = 3x!x = 10! !Hence speed of boat in still water is 10 Km/h.

#### Question No 47

A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

Solution!
Speed = (240/24) = 10m/s! !Hence, Required time = (240+650)/10!= 89 seconds.

#### Question No 48

A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is

Solution!
Let the length of the train be x metres and its speed by y m/sec.! !Then, x/y = 15!y = x/15! !So, (x+100)/25 = x/15!15(x + 100) = 25x!15x + 1500 = 25x!1500 = 10x!x = 150 m.

#### Question No 49

A boat covers a certain distance downstream in 1 hour, while it comes back in 1.5 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?

Solution!
Let the speed of the boat in still water be x kmph.! !Then,!Speed downstream = (x + 3) kmph! !Speed upstream = (x - 3) kmph! !So, (x + 3) * 1 = (x - 3)* 3/2!2x + 6 = 3x - 9! !Hence, x = 15 kmph.

#### Question No 50

A train 110 meters long passses telegraph pole in 3 seconds. How long will it take to cross a platform 165 meters long?

Solution!
Length of the train = L1 = 110m!Time = t1 = 3s! !v = L1/t!v = 110/3! !Length of the platform = L2 = 165m! !t2 = (L1+L2)/v!By putting values!t2 = (110+165)*(3/110)!t2 = 7.5s! !Hence it will take 7.5 seconds to cross the platform..

#### Question No 51

A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is

Solution!
Man's rate in still water = (15 - 2.5) km/hr!= 12.5 km/hr! !Man's rate against the current = (12.5 - 2.5) km/hr!= 10 km/hr.

#### Question No 52

David can swim at the speed of 30 km/h in still water and speed of water is 4 km/h. What is his speed of swimming against the direction of water?

Solution!
David's speed in still water = u = 30 Km/h!Speed of water = v = 4 Km/h!David's swimming speed against water = u-v = 30-4 = 26 Km/h.

#### Question No 53

A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is

Solution!
Let the speed of the stream x mph.! !Then,!Speed downstream = (10 + x) mph! !Speed upstream = (10 - x) mph! !So, [36/(10 - x)] - [36/(10 + x)] = 90/60!(72x)*60 = 90 (100 - x*x)!(x+ 50)(x - 2) = 0! !Hence, x = 2 mph..

#### Question No 54

A train travelling at he speed of 72km/h can cross a platform in 17 seconds. If length of the train is 180 meters, what is the length of the platform?

Solution!
Speed of train = v = 72Km/h = 72*(5/18) = 20m/s! !Time = t = 17s!Length of the train = L1 = 180m!Length of the platform = L2 = ?! !t = (L1+L2)/v!By putting values!17 = (180+L2)/20!340-180 = L2!L2 = 160m! !Hence length of the platform is 160m..

#### Question No 55

The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is

Solution!
Speed = 45 * (5/18)!= 25/2 m/s! !Time = 30 sec! !Let the length of bridge be x metres! !Then,!(130 + x)/30 = 25/2!2(130 + x) = 750! !Hence, x = 245 m.

#### Question No 56

A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is

Solution!
Let the speed of the second train be x km/hr.! !Relative speed = (x + 50) km/hr!= (x+50)*(5/18) m/s!= (250+5x)18 m/s! !Distance covered = (108 + 112) = 220 m! !So, 220/[(250 + 5x) /18] = 6!250 + 5x = 660! !Hence, x = 82 km/hr.

#### Question No 57

A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

Solution!
Let the length of the train be x metres and its speed by y m/sec.! !Then,!x/y = 8!x = 8y! !Now, (x+264)/20 = y!8y + 264 = 20y!y = 22! !Hence, Speed = 22 m/sec!= 22 * (18/5)!= 79.2 km/hr.

#### Question No 58

A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?

Solution!
Rate downstream = (1/10) * 60 km/hr = 6 km/hr! !Rate upstream = 2 km/hr! !Speed in still water = (1/2)(6 + 2) km/hr = 4 km/hr! !Hence, Required time = 5/4 hrs = 1 hr 15 min..

#### Question No 59

A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

Solution!
Relative speed = (120 + 80) km/hr!= 200(5/18)m/s!= (500/9)m/s! !Let the length of the other train be x metres! !Then,!(x+270)/9 = 500/9!x + 270 = 500! !Hence, x = 230.

#### Question No 60

A ship travels at the speed of 20 km/h upstream and 24 km/h downstream. What is the speed of boat in still water?