Multiple choice

The distance from Joshua's home to school is 4 miles, which he covers by walking. On Tuesday, Joshua covered 50% of the distance at an average speed of 5 miles per hour, and after covering the 50% distance, Joshua realized that he was getting late for school and started running. At what average speed must Joshua run so that his average speed for the entire distance becomes 6 miles per hour? (Joshua did not stop anywhere on the way from his home to school.)

  1. 7 mph

  2. 8 mph

  3. 7.5 mph

  4. 8.5 mph

  5. 9 mph
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total distance is 4 miles. First 2 miles at 5 mph takes 0.4 hours. To average 6 mph over 4 miles, total time must be 4/6 = 2/3 hours. Remaining 2 miles must be covered in (2/3 - 0.4) = 0.2667 hours. Speed = 2 / 0.2667 = 7.5 mph.

AI explanation

To cover the 4 miles at an average speed of 6 mph, Joshua must complete the entire journey in 4/6 hours, or 40 minutes. He walks 2 miles at 5 mph, taking 2/5 hours, which equals 24 minutes, leaving him 16 minutes (or 4/15 hours) to run the remaining 2 miles. Dividing the remaining distance by the remaining time gives a required running speed of 2 divided by 4/15, which equals 7.5 mph.

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