FILE No.69Unsolved
A suspect, Miller, says: "I drove from home to a beach house and back along the same road, 60 mph on the way out and 40 mph on the way back." The road is 120 miles each way.
The crime happened while Miller was away. To work out how long the trip took, the police want the average speed.
Miller says: "The average is (60 + 40) / 2 = 50 mph."
What is the average speed for the round trip?
If you get stuck, open the hints one at a time, in order.
How long did each leg take?
What was the total distance?
Average speed = total distance / total time.
What is the average speed for the round trip?
Choose the answer closest to the truth.
48 mph
The answer is: 48 mph.
The trip out takes 120 / 60 = 2 hours. The trip back takes 120 / 40 = 3 hours. Total distance 240 miles, total time 5 hours, so the average speed is 240 / 5 = 48 mph.
It is not 50 because more time was spent at the slower speed. Average speed is total distance divided by total time, not the average of the speeds.
"The middle of 60 and 40 is 50" sounds so natural that it passes as the answer.
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