A bike messenger delivers a package from the courthouse to a law firm downtown, traveling at an average speed of 24 miles per hour. On the way back, the bike messenger gets stuck in traffic, which reduces his average speed for the return trip by 12.5 percent . What was the bike messenger's average speed, in miles per hour, for the round trip?

Options

A. `22`
B. `22.1`
C. `22.4`
D. `22.5`

Answer

C

Explanation

Difficult: Medium
Category: Problem Solving and Data Analysis/ Rates, Ratios, Proportions, and Percentages
Strategic Advice: In average speed problem, never take the average of the two average speeds. Instead, use the formula:
Average speed`=("total distance")/("total time")`
Getting to the Answer: The bike messenger's average speed in one direction is 24 mph. On the way back, it's reduced by 12.5% or `0.125times24=3` mph, for an average speed of 21mph. The answer is NOT the average speed of these two speeds, 22.5, because that fails to account for the facts that the bike messenger spent more time traveling at the slower speed. Instead, use the average speed formula to find the answer.
You're not given the distances to the law firm, so pick a convenient number to use in your calculations. A goog number to pick is 169 because it's divisible by both 21 and 24. Given that Time`=("distance")/("speed")`, the times spent travelling form the courthouse is `(168)/(24)=7` hours, and the times spent travelling back is `(168)/(21)=8` hours, for a total time of `7+8=15` hours. The total distance there and back is `168+168=336` miles. You now have enough information to use the average speed formula: Average speed=`("total distance")/("total times")=(336)/(15)=22.4`, choice (C).