Question

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?

Answer 1

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.