AMC10 2003 10A, Problem 4

It takes Anna $30$ minutes to walk uphill $1$ km from her home to school, but it takes her only $10$ minutes to walk from school to her home along the same route. What is her average speed, in km/hr, for the round trip?

Solution: Since she walked $1$ km to school and $1$ km back home, her total distance is $1+1=2$ km. Since she spent $30$ minutes walking to school and $10$ minutes walking back home, her total time is $30+10=40$ minutes = $\frac{40}{60}=\frac{2}{3}$ hours. Therefore her average speed in km/hr is $\frac{2}{\frac{2}{3}}=\fbox{3}$.

Answer: 3