Time, Speed & Distance

Question No 1

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 2

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 3

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 4

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 5

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 6

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 7

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 8

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 9

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 10

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 11

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 12

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 13

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 14

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 15

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 16

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 17

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 18

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 19

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 20

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 21

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 22

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 23

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 24

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 25

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 26

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 27

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 28

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?

Solution!
Upstream speed = y = 20 Km/h
Downstream speed = x = 24 Km/h
Speed of ship = (1/2)*(x+y)
=(1/2)*(20+24) = 22 Km/h.

Question No 29

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 30

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 31

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 32

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 33

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 34

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 35

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 36

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 37

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 38

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 39

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 40

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 41

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 42

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 43

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 44

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 45

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 46

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 47

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 48

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 49

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 50

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 51

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 52

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 53

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 54

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 55

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 56

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 57

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 58

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 59

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 60

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.
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