Circular gears P and Q start rotating at the same time at co

[hifunda_88]

Taking inspiration from the above solutions, here's another very similar way for straightforward algebra lovers:

We want the time taken for Gear Q to make 6 more revolutions than gear P:

Distance covered by P = rxt = 40rev/min x T = 40T
Distance covered by Q = rxt = 10 rev/min x T = 10T

Therefore, Q's distance = 6 + P's distance.
10T = 40T + 6
Solve for T: 30T=6, or T=1/5 minutes.
Convert to seconds: T= 1/5x60 = 12 seconds.

[jlucero]

A lot of great ways of thinking about this problem. Notice the math ends up being the same, because you are all thinking of different ways of starting the problem, but finding the same answer.