Question

if a runner who runs at a constant speed of p miles per hour runs a mile in exactly p minutes what is the integer closest to the value p

Answer 1

The value of p is 7.746. The nearest integer is 8.

Explanation:

The speed of the runner is p miles per hour.

`1\text{ hour}=p\text{ miles}`

The speed formula is

`speed=(distance)/(time)`

It is given that he runs a mile in exactly p minutes. We know that

`1\text{ hour}=60\text{ minutes}`

So, we get

`speed=(1)/((p)/(60))`

`speed=(60)/(p)`

Since the speed is p.

`p=(60)/(p)`

`p^2=60`

Taking square both sides.

`p=√(60)=7.746`

Therefore the value of p is 7.746. The nearest integer is 8.