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George drives to work at a rate of 25 mph and cycles home after school at a rate of 10 mph. It takes him 36 more minutes to cycle home than drive to school. how far is george's home from his school?

User Bergin
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1 Answer

2 votes

Answer:

10 miles

Explanation:

Given


\displaystyle \text{Time}=\frac{\text{Distance}}{\text{Speed of Driving}}=\frac{\text{Distance}}{\text{25\,\text{mph}}}


\displaystyle \text{Time}=\frac{\text{Distance}}{\text{Speed of Cycling}}=\frac{\text{Distance}}{\text{10\,\text{mph}}}


36\,\text{minutes}=0.6\,\text{hours}

Create an equation and solve


\displaystyle \text{Driving Time}+\text{Extra Time}=\text{Cycling Time}\\\\\frac{\text{Distance}}{\text{Speed of Driving}}+0.6=\frac{\text{Distance}}{\text{Speed of Cycling}}\\\\\frac{\text{Distance}}{25}+0.6=\frac{\text{Distance}}{10}\\\\2*\text{Distance}+30=5*\text{Distance}\\\\30=3*\text{Distance}\\\\10=\text{Distance}

Therefore, George's home is 10 miles from his school.

User Karla
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