Question

Arun leaves his home and drives at a speed of 18 km per hour, reaching the railway station 25 minutes after the train had departed. If instead, he had driven at a speed of 20 km per hour, he would have reached the station 5 minutes before the train's departure. The distance (in km) from his home to the railway station is: ______

Answer 1

By setting the distance traveled in two scenarios with different speeds equal, we can solve the corresponding time speed equations to find that the distance from Arun's home to the railway station is 6 kilometers.

Step-by-step explanation:

The distance from Arun's home to the railway station can be calculated using the concept of relative speed and time difference. When Arun drives at 18 km/h, he reaches the station 25 minutes after the train has departed. Had he driven at 20 km/h, he would have reached 5 minutes before the train departed.

This gives us an overall time difference of 30 minutes or 0.5 hours between the two scenarios. We can set up two equations based on the formula distance = speed × time for each scenario and solve for the distance.

Equations

1. distance = 18 km/h × (t + 25/60 hr)
2. distance = 20 km/h × (t - 5/60 hr)

Here, t is the time at which the train departs. Since the distances in both equations are the same, we can set the right-hand sides of both equations equal and solve for t, then use either equation to find the distance.

After solving the equations, we find the distance from Arun's home to the railway station is 6 kilometers.