Question

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?

Answer 1

18 km

Step-by-step 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.

`1\ min = (1)/(60)\ h\\5\ min =(5)/(60)=(1)/(12)\ h`

So, time is
`x+(1)/(12)`

Therefore,

`x+(1)/(12)=(d)/(24)\\\\x=(d)/(24)-(1)/(12)\\\\x=(1)/(12)((d)/(2)-1)---------1`

Now, when speed is 30 km/h, time is reduced by 4 minutes or
`(4)/(60)=(1)/(15)\ hours`

So, time now is
`x-(1)/(15)`

Again using the time formula, we have

`x-(1)/(15)=(d)/(30)\\\\x=(d)/(30)+(1)/(15)\\\\x=(1)/(15)((d)/(2)+1)-------------2`

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

`(1)/(12)((d)/(2)-1)=(1)/(15)((d)/(2)+1)\\\\(15)/(12)((d)/(2)-1)=(d)/(2)+1\\\\(5d)/(8)-(5)/(4)=(d)/(2)+1\\\\(5d)/(8)-(d)/(2)=1+(5)/(4)\\\\(5d-4d)/(8)=(4+5)/(4)\\\\(d)/(8)=(9)/(4)\\\\d=(9* 8)/(4)=(72)/(4)=18\ km`

Therefore, the office is 18 km from his house.