 # Time & Distance (6)

1. A train , 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel (in meters)?
1. 440 m
2. 500 m
3. 260 m
4. 430 m

Explanation :-

Let length of tunnel is x meter
Distance = (800+x)meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = (78*5/18) m/s = 65/3 m/s
Distance = Speed*Time
(800 + x) = (65/3)*60
(800 x) = 20*65
800 + x = 1300
x = 500
Therefore , the length of the tunnel = 500 meters.

2. Two train each 500 m long, are running in opposite directions on parallel tracks. If their speeds are 45 km/hr and 30 km/hr respectively, the time taken by the slower train to pass the driver of the faster one is
1. 50 sec
2. 58 sec
3. 24 sec
4. 22 sec

Explanation :-

Relative Speed = 45 + 30 = 75 km/h = 750/36 m/s = 125/6 m/s
Distance = Length of the smaller train
Time = Distance/Speed = 500/(125/6) = 24 s

3. Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. If the fast train completely passes a man sitting in the slower train in 5 seconds, the length of the fast train is :
1. 19 m
2. 27 7/9 m
3. 13 2/9 m
4. 33 m

Explanation :-

As Trains are moving in same direction,
So, Relative Speed = 40-20 = 20 km/h = 20*(5/18) = 50/9 m/sec
Length of Train= Speed * Time
Length of train = (50/9)*20 = 250/9 = 27 7/9 m

4. Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is
1. 42
2. 36
3. 28
4. 20

Explanation :-

Distance covered = 120+120 = 240 m
Time = 12 s
Let the speed of each train = x m/s
Therefore ,
Relative speed = x + x = 2x
Speed = Total distance/Time
2x = 240/12 = 20 m/s
x = 10 m/s
Speed of each train = 10 m/s
= 10 × 36/10 km/hr = 36 km/hr

5. A train 108 m long is moving at a speed of 50 km/hr . It crosses a train 112 m long coming from opposite direction in 6 seconds. What is the speed of the second train?
1. 82 kmph
2. 76 kmph
3. 44 kmph
4. 58 kmph

Explanation :-

Speed of 1st Train = 50 km/h
Let the speed of Second train = x km/h
Relative Speed = (x +50) km/h = (x + 50) (5/18) m/s = (5x + 250)/18 m/s
Distance Covered = (108 + 112) = 220 m
Speed = distance / Time
(5x + 250)/18 = 220 / 6
5x + 250 = 660
5x = 410   =>   x = 82 km/h