A train running at a speed of 60 km/hr takes 24 sec to pass a tunnel. Also,it…

Given:

A train running at a speed of 60 km/hr takes 24 sec to pass a tunnel

It takes 15 sec to pass a man walking at 6 km/hr in the same direction in which the train is going

Concept:

Consider the two cases seperately, and find train length first. Relative speed in same direction will be the difference of individual speeds

Formula used:

Speed = Distance/Time

Calculation:

Let the length of the train be x

The train takes 15 sec to pass a man walking at 6 km/hr in the same direction in which the train is going

Relative speed = 60 - 6 = 54 km/hr

⇒ 54 km/hr = 54 × (5/18) = 15 m/s

Speed = Distance/Time

15 = x/15

⇒ x = 15 × 15 = 225 m

∴ Length of the Train = 225 m

Now, train running at a speed of 60 km/hr takes 24 sec to pass a tunnel

Let the length of the tunnel be y

Speed = 60 km/hr = 60 × (5/18) = 50/3 m/s

50/3 = (y + 225)/24

⇒ y + 225 = 24 × (50/3) = 400

∴ y = 400 - 225 = 175 m

Length of the Tunnel = 175 m

The length of the train and the length of the tunnel are 225 m and 175 m respectively