Multiple choice

A long-distance runner is training for a marathon. On the half of his 21-mile training run, he maintains an average speed of 6 miles per hour. To achieve his goal of averaging 7 miles per hour for the entire run, at what average speed (in miles per hour) must he complete the remaining 10.5 miles of the run?

  1. 7.2 miles per hour

  2. 8.4 miles per hour

  3. 9.4 miles per hour

  4. 9.8 miles per hour

  5. 10.4 miles per hour
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total distance = 21 miles. Goal speed = 7 mph. Total time = 21 / 7 = 3 hours. First half (10.5 miles) at 6 mph takes 10.5 / 6 = 1.75 hours. Remaining time = 3 - 1.75 = 1.25 hours. Required speed for remaining 10.5 miles = 10.5 / 1.25 = 8.4 mph.

AI explanation

The total distance of 21 miles at an average speed of 7 mph will take exactly 21 / 7 = 3 hours. The first 10.5 miles at 6 mph takes 10.5 / 6 = 1.75 hours, leaving 3 - 1.75 = 1.25 hours for the remaining 10.5 miles. Dividing the remaining distance by the remaining time gives the required speed: 10.5 / 1.25 = 8.4 miles per hour.

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