A soccer coach riding his bike reaches his office in xx hours. If he travels at 24 km/h, he reaches his office 5 minutes late. If he travels 30 km/h, he reaches his office 4 minutes early. How far is his office from his house?

18 km

Explanation:

Let 'd' be the distance between his house and office.

Normal time taken to reach the office = 'x' hours.

If speed is 24 km/h, time is increased by 5 minutes.

If speed is 30 km/h, time is reduced by 4 minutes.

We know that,

Time taken = Distance traveled ÷ Speed

So, when speed is 24 km/hr, time is increased by 5 minutes.

So, time is

Therefore,

Now, when speed is 30 km/h, time is reduced by 4 minutes or

So, time now is

Again using the time formula, we have

Equations (1) and (2) are equal. So,

Therefore, the office is 18 km from his house.