## 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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2022-02-10T14:31:21+00:00
2022-02-10T14:31:21+00:00 1 Answer
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## Answers ( )

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 [tex]x+5[/tex] miles per hour.

[tex]\text{Distance}=\text{Rate}\cdot \text{Time}[/tex]

10 minutes = 1/6 hour.

20 minutes = 1/3 hour

While walking, we will get [tex]D_{\text{walking}}=x\frac{\text{miles}}{\text{hour}}\cdot \frac{1}{3}\text{hour}[/tex]

[tex]D_{\text{walking}}=\frac{x}{3}[/tex]

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

[tex]D_{\text{jogging}}= \frac{(x+5)}{6}[/tex]

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

[tex]\frac{x}{3}=\frac{x+5}{6}[/tex]

Cross multiply:

[tex]6x=3x+15[/tex]

[tex]6x-3x=15[/tex]

[tex]3x=15[/tex]

[tex]\frac{3x}{3}=\frac{15}{3}\\\\x=5[/tex]

Therefore, athlete’s walking speed is 5 miles per hour.Jogging speed: [tex]x+5\Rightarrow 5+5=10[/tex]

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