Problem:
Austin and itemple are miles apart along Interstate . Bonnie drove from Austin to her daughter's house in itemple, averaging miles per hour. Leaving the car with her daughter, Bonnie rode a bus back to Austin along the same route and averaged miles per hour on the return trip. What was the average speed for the round trip, in miles per hour?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Find the time traveling to Temple by dividing the distance, miles, by the rate, miles per hour: hours. Find the time returning by dividing the distance, miles, by the rate, miles per hour: hours. Find the average speed for the round trip by dividing the total distance, miles, by the total time, hours. The average speed is miles per hour.
NOTE: The harmonic mean of numbers and is found using the formula . The harmonic mean is the average rate if the same distance is traveled at two different rates.
If and , then miles per hour.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions