Question

An athlete knows that when she jogs along her neighborhood​ greenway, she can complete the route in 10 minutes. It takes 20 minutes to cover the same distance when she walks. If her jogging rate is 5 mph faster than her walking​ rate, find the speed at which she jogs.

Answer 1

Answer:

10 miles per hour.

Step-by-step explanation:

Let x represent athlete's walking speed.

We have been given that her jogging rate is 5 mph faster than her walking​ rate, so athlete's jogging speed would be $x+5$ miles per hour.

$\text{Distance}=\text{Rate}\cdot \text{Time}$

10 minutes = 1/6 hour.

20 minutes = 1/3 hour

While walking, we will get $D_{\text{walking}}=x\frac{\text{miles}}{\text{hour}}\cdot \frac{1}{3}\text{hour}$

$D_{\text{walking}}=\frac{x}{3}$

While jogging, we will get $D_{\text{jogging}}=(x+5)\frac{\text{miles}}{\text{hour}}\cdot \frac{1}{6}\text{hour}$

$D_{\text{jogging}}= \frac{(x+5)}{6}$

Since athlete is covering same distance while walking and jogging, so we can equate both expressions as:

$\frac{x}{3}=\frac{x+5}{6}$

Cross multiply:

$6x=3x+15$

$6x-3x=15$

$3x=15$

$\frac{3x}{3}=\frac{15}{3}\\\\x=5$

Therefore, athlete's walking speed is 5 miles per hour.

Jogging speed: $x+5\Rightarrow 5+5=10$

Therefore, athlete's jogging speed is 10 miles per hour.