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

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    2022-02-10T14:32:39+00:00

    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.

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