Question

Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute, and gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

Answer 1

12 seconds

Explanation:

The difference in rotation rate is 40 - 10 = 30 rev/min. That means the faster gear makes one more revolution in 1/30 minute = 2 seconds. For 6 more revolutions, it will take 6×(2 seconds) = 12 seconds.

___

In 12 seconds = 1/5 minute, P makes 10/5 = 2 revolutions; Q makes 40/5 = 8 revolutions. 8 is 6 more than 2.