## 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

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.

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3 months 2022-02-10T14:31:21+00:00 1 Answer 0 views 0

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.