An emergency vehicle travels 10 miles at a speed of 50 miles per hour. How…

For a multi-leg journey with a fixed total travel-time budget, each leg's time equals Distance divided by Speed, and the times of all legs together must add up to the total time budget. So the speed required for an unknown leg is found by first working out how much of the total time genuinely remains for it, then applying Speed = Distance divided by Time to that leg alone.

1. Time taken for the outbound leg = 10 miles ÷ 50 miles per hour = 1/5 hour = 12 minutes.

2. Time available for the return leg = total round-trip time − outbound leg time = 20 minutes − 12 minutes = 8 minutes = 8/60 hour = 2/15 hour.

3. Required return speed = Distance ÷ Time = 10 miles ÷ (2/15 hour) = 10 × 15/2 = 75 miles per hour.

Checking backwards: at 75 miles per hour, the 10-mile return leg takes 10/75 hour = 8 minutes; adding the 12 minutes taken for the outbound leg gives exactly 20 minutes, matching the stated round-trip time — confirming 75 miles per hour.