Respuesta :
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.
