Question

Austin and Temple are $50$ miles apart along Interstate $35.$ Bonnie drove from Austin to her daughter's house in Temple, averaging $60$ miles per hour. Leaving the car with her daughter, Bonnie rode a bus back to Austin along the same route and averaged $40$ miles per hour on the return trip. What was the average speed for the round trip, in miles per hour?

$46$

$48$

$50$

$52$

$54$

Solution:

The trip from Austin to Temple took $50 \div 60 = \dfrac{5}{6}$ hours. The trip from Temple to Austin took $50 \div 40 = \dfrac{5}{4}$ hours. This means that the total time for the round trip was $\dfrac{5}{6} + \dfrac{5}{4} = \dfrac{25}{12}$ hours.

The total distance of the round trip was $2 \cdot 50 = 100$ miles. Therefore, the average speed for the round trip was $100 \div \dfrac{25}{12} = 48$ miles per hour.

Thus, B is the correct answer.

2009 AMC 8 Problem 14

Solution:

Problem 14 in Other Years