TIME AND DISTANCE - 2

Case - II: If both the bodies are moving in the same direction

If two bodies are moving in the same direction then the relative speed of them
= difference of their speeds
Example: A train leaves Mumbai at 9 a.m at a speed of 40 kmph. After one hour another
train leaves Mumbai in the same direction as that of the first train at a speed of
50 kmph. When and at what distance from Mumbai do the two trains meet?
1) 1.00 p.m., 220 km 2) 1.00 p.m., 200 km
3) 2.00 p.m., 200 km 4) 2.00 p.m., 160 km
23. Two trains for Mumbai leave Delhi at 10 am and 10.30 am and travel at the speeds of 60
kmph and 75 kmph respectively. How many kilometers from Delhi will the two trains be
together.
(a) 250 km (b) 200 km (c)150 km (d) 100 km
24. A train X starts from Meerut at 4 p.m. and reaches Ghaziabad at 5 p.m. while another
train Y starts from Ghaziabad at 4 p.m. and reaches Meerut at 5:30 p.m. The two trains
will cross each other at:
(a) 4:36 p.m. (b) 4:42 p.m. (c) 4:48 p.m. (d) 4:50 p.m.
 Problems Based on Trains

Case - I: Train crossing a stationery object

Type - 1: Train crossing an electric pole / a standing man / a tree etc…
Type - 2: Train crossing a platform / bridge / tunnel etc…
Example: What is the time taken by a 320 m long train travelling at 72 kmph to cross
i) an electric pole
ii) a 240 m long bridge
iii) a 420 m long tunnel
16. A Train requires 7 seconds to pass a pole while it requires 25 seconds to cross a
stationary train which is 378 m long. Find the speed of the train.
(a) 75.6 kmph (b) 75.4 kmph (c) 76.2 kmph (d) 21 kmph
Example: A train that is 280 metres long, travelling at a uniform speed, crosses a platform in
60 seconds and passes a man standing on the platform in 20 seconds. What is the
length of the platform in metres?
a) 560 b) 840 c) 280 d) 1120
17. A train running with 40 m/sec crosses a bridge in 30 seconds and a man on the bridge in
10 seconds and a man on the bridge in 10 seconds. Find the train length and bridge
length?
(a) 400m; 800m (b) 200m; 600m (c) 500m:1500m (d) None
 Problems Based on Trains

Case - II: Train crossing a moving object

Type - 1: Train crossing a moving man/ cyclist / motorist / car / bus / truck etc…
19. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine
of a 120 metres long train running at 45 kmph in the same direction. In how much time
will the train pass the jogger
(a) 3.6 sec (b) 18 sec (c) 36 sec (d) 72 sec
18. From the time the front of a train enters a platform, it takes 25 seconds for the back of
the train to leave the platform, while travelling at a constant speed of 54 km/h. At the
same speed, it takes 14 seconds to pass a man running at 9 km/h in the same directions
as the train. What is the length of the train and that of the platform in meters,
respectively? (GATE - 18)
(a) 210 and 140 (b) 162.5 and 187.5 (c) 245 and 130 (d) 175 and 200
Type - 2: Train crossing another moving train
Example:Two trains travel in the same direction at the speeds of 56 kmph and 29 kmph
respectively. The faster train passes a man in the slower train in 32 seconds. The
length of the faster train (in metres) is
a) 240 b) 480 c) 320 d) 260
Example: Two trains one 480 m and the other 420 m long are running in opposite directions
on parallel rails, the first at 77 km an hour and the other at 67 km an hour. How
long will they take to cross each other?
a) 21sec b) 22.5 sec c) 18 sec d) 30 sec
Example: A 432 m long train travelling at 59 kmph crosses another train coming in opposite
direction at 67 kmph in 24 seconds. The length of the second train in metres is
a) 408 b) 426 c) 384 d) 432
Example: Two trains are running in opposite direction with the same speed. If the length of
each train is 120 metres and they cross each other in 12 seconds, the speed of each
train (in kmph) is
a) 72 b) 10 c) 36 d) 18
26. Speed of a boat in still water is 16 km/h. If it can travel 20 km downstream in the same
time as it can travel 12 km upstream, the rate of stream is
(a) 1 km/h (b) 2 km/h (c) 4 km/h (d) 5 km/h
29. If Boat's rate in still water is 20 km/hr and it takes him thrice as long to row up as to row
down the river. Find the stream rate?
(a) 10 km/hr (b) 12 km/hr (c) 5 km/hr (d) 8 km/hr
27. If boats rate in still water is 20 km/hr and stream rate is 10 km/hr, and it takes him 10
hrs to row to a place and back, then how for is the place?
(a) 75 kms (b) 60 kms (c) 70 kms (d) 40 kms
28. If boats's rate in still water is 10 km/hr and river is flowing with a certain speed, it takes
him 20 hrs to row to a place and back and the length of the river is 75 kms. Then find the
velocity of water?
(a) 10 km/hr (b) 15 km/hr (c) 7 km/hr (d) 5 km/hr