Speed Time Distance Problems Part 2

Speed Time Distance Problems Part 2


16. 
A train travelling at a speed of 75 mph enters a tunnel 31/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
A.2.5 min
B.3 min
C.3.2 min
D.3.5 min
Answer: Option B
Explanation:
Total distance covered
=(7+1(miles
24
=15miles.
4
Therefore Time taken
=(15(hrs
4 x 75
=1hrs
20
=(1x 60(min.
20
= 3 min.
17. 
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:
A.130
B.360
C.500
D.540
Answer: Option C
Explanation:
Speed =(78 x5(m/sec=(65(m/sec.
183
Time = 1 minute = 60 seconds.
Let the length of the tunnel be x metres.
Then,(800 + x(=65
603
=> 3(800 + x) = 3900
=> x = 500.
18. 
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?
A.320 m
B.350 m
C.650 m
D.Data inadequate
Answer: Option B
Explanation:
Speed =(300(m/sec =50m/sec.
183
Let the length of the platform be x metres.
Then,(x + 300(=50
393
=> 3(x + 300) = 1950
=> x = 350 m.
19. 
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
A.50 m
B.150 m
C.200 m
D.Data inadequate
Answer: Option B
Explanation:
Let the length of the train be x metres and its speed by y m/sec.
Then,x= 15     =>     y =x.
y15
Thereforex + 100=x
2515
=> 15(x + 100) = 25x
=> 15x + 1500 = 25x
=> 1500 = 10x
=> x = 150 m.
20. 
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?
A.69.5 km/hr
B.70 km/hr
C.79 km/hr
D.79.2 km/hr
Answer: Option D
Explanation:
Let the length of the train be x metres and its speed by y m/sec.
Then,x= 8     =>     x = 8y
y
Now,x + 264y
20
=> 8y + 264 = 20y
=> y = 22.
Therefore Speed = 22 m/sec =(22 x18(km/hr = 79.2 km/hr.
5

21. 
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?
A.25
B.30
C.40
D.45
Answer: Option B
Explanation:
Speed of the train relative to man= (63 - 3) km/hr
= 60 km/hr
=(60 x5(m/sec
18
=(50(m/sec.
3
Therefore Time taken to pass the man
=(500 x3(sec
50
= 30 sec.
22. 
Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
A.12 sec
B.24 sec
C.48 sec
D.60 sec
Answer: Option B
Explanation:
Relative speed == (45 + 30) km/hr
=(75 x5(m/sec
18
=(125(m/sec.
6
We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.
So, distance covered = Length of the slower train.
Therefore, Distance covered = 500 m.
Therefore Required time =(500 x6(= 24 sec.
125
23. 
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 (in km/hr) is:
A.10
B.18
C.36
D.72
Answer: Option C
Explanation:
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.
Therefore Speed of each train = 10 m/sec =(10 x18(km/hr = 36 km/hr.
5
24. 
Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
A.10
B.12
C.15
D.20
Answer: Option B
Explanation:
Speed of the first train =(120(m/sec = 12 m/sec.
10
Speed of the second train =(120(m/sec = 8 m/sec.
15
Relative speed = (12 + 8) = 20 m/sec.
Therefore Required time =[(120 + 120)]sec = 12 sec.
20
25. 
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:
A.48 km/hr
B.54 km/hr
C.66 km/hr
D.82 km/hr
Answer: Option D
Explanation:
Let the speed of the second train be x km/hr.
Relative speed= (x + 50) km/hr
=[(x + 50) x5]m/sec
18
=[250 + 5x]m/sec.
18
Distance covered = (108 + 112) = 220 m.
Therefore220= 6
(250 + 5x(
18
=> 250 + 5x = 660
=> x = 82 km/hr.
26. 
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
A.23 m
B.
232m
9
C.
277m
9
D.29 m
Answer: Option C
Explanation:
Relative speed = (40 - 20) km/hr =(20 x5(m/sec =(50(m/sec.
189
Therefore Length of faster train =(50x 5(m =250m = 277m.
999
27. 
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:
A.45 m
B.50 m
C.54 m
D.72 m
Answer: Option B
Explanation:
2 kmph =(2 x5(m/sec =5m/sec.
189
4 kmph =(4 x5(m/sec =10m/sec.
189
Let the length of the train be x metres and its speed by y m/sec.
Then,(x(= 9 and(x(= 10.
y -5
9
y -10
9
Therefore 9y - 5 = x and 10(9y - 10) = 9x
=> 9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50.
Therefore Length of the train is 50 m.
28. 
A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
A.66 km/hr
B.72 km/hr
C.78 km/hr
D.81 km/hr
Answer: Option D
Explanation:
4.5 km/hr =(4.5 x5(m/sec =5m/sec = 1.25 m/sec, and
184
5.4 km/hr =(5.4 x5(m/sec =3m/sec = 1.5 m/sec.
182
Let the speed of the train be x m/sec.
Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5
=> 8.4x - 10.5 = 8.5x - 12.75
=> 0.1x = 2.25
=> x = 22.5
Therefore Speed of the train =(22.5 x18(km/hr = 81 km/hr.
5
29. 
A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
A.400 m
B.450 m
C.560 m
D.600 m
Answer: Option A
Explanation:
Let the length of the first train be x metres.
Then, the length of the second train is(x(metres.
2
Relative speed = (48 + 42) kmph =(90 x5(m/sec = 25 m/sec.
18
Therefore[x + (x/2)]= 12 or3x= 300     or     x = 200.
252
Therefore Length of first train = 200 m.
Let the length of platform be y metres.
Speed of the first train =(48 x5(m/sec =40m/sec.
183
Therefore (200 + y) x3= 45
40
=> 600 + 3y = 1800
=> y = 400 m.
30. 
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
A.9 a.m.
B.10 a.m.
C.10.30 a.m.
D.11 a.m.
Answer: Option B
Explanation:
Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
=> 45x = 135
=> x = 3.
So, they meet at 10 a.m.


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