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?

GMAT PREP EXAM 1

The correct answer is 12.

Could someone solve this problem so I can compare to what I got. I just want to make sure I understand this problem. Your input is greatly appreciated...

P-> 10 rev/ min, i.e. 10 rev/60 sec = 1 rev in 6 secs or it takes 6 secs to take 1 rev.
Q-> 40 rev/ min, i.e. 60 rev/60 sec = 4 rev in 6 secs or it takes 6 secs to take 4 rev.

Please see that in 6 secs Q takes a lead of 3 revs when compared to A. Therefore in 12 secs, the lead will be by 6revs. Hence answer is 12secs :wink:

(40/60 -10/60)*T =6
1/2 T =6
T =12

the solutions posted above are good - one intuitive, one algebraic - and i don't have much to add to them. if you need further explanation, especially of the genesis of the algebraic solution, post back and i can flesh it out a little bit.

with numbers like this, you could also just 'grind' the problem until you find numbers that work.
specifically:
gear p makes ten revolutions per minute, so that's one revolution every 6 seconds.
gear q rotates four times as fast, so that's four revolutions every 6 seconds.

just make a table until you get a difference of 6 revs:

seconds ... revs P ... revs Q
6 ............... 1 ........... 4
12 .............. 2 ........... 8
we have a winner.

this method has obvious limitations, and will crash and burn if the problem contains numbers less friendly than the ones here, but it works admirably in this particular case.