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

Answer:

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

Step-by-step explanation:

The speed of the runner is p miles per hour.

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

The speed formula is

$speed=\frac{distance}{time}$

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

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

So, we get

$speed=\frac{1}{\frac{p}{60}}$

$speed=\frac{60}{p}$

Since the speed is p.

$p=\frac{60}{p}$

$p^2=60$

Taking square both sides.

$p=\sqrt{60}=7.746$

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