GMAT Math question please help!?

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?

Thank you!

Answer 1

Let's calculate the number of rotations needed and then the amount of time.

p = Number of rotations for gear P
q = Number of rotations for gear Q

q = 4p
q = p + 6

4p = p + 6
3p = 6
p = 2 revolutions

Gear P makes 10 revolutions / minute = 6 seconds / revolution

Time = (2 revolutions)(6 seconds / revolution) = 12 seconds

Answer 2

Every minute, gear Q makes 30 more revolutions than P (40-10=30). Since the rates are constant, Q would make 6 more revolutions in 1/5 min (30/6=5). 1/5 min is 12 sec (60/5=12).

12 sec.

Answer 3

gear p = 10/60 = 1/6 rev/sec

gear q = 40/60 = 2/3 rev/sec

so at 6 seconds gear p has made 1 revolution and gear q has made 4 revs

at 12 gear p is at 2 and gear q is at 8

your answer is 12 seconds

Answer 4

If Gear P makes 10 rpm, then it revolves once every six seconds. Gear Q, at 40 rpm, will revolve 4 times every six seconds, or 4 times as fast.

Let t = time. After t seconds, P will have revolved t/6 times, and Q will have revolved 4t/6 times. Set up your equation:

4t/6 - 6 = t/6
(Or, at what time t will Q have revolved six times more than P?)

Solving for t:

4t/6 - 6 = t/y
4t - 36 = t
3t - 36
t = 12 seconds

At 12 seconds, P will have revolved 2 times, and Q will have revolved 8 times.

Hope that helps.

Answer 5

Okay, set it up as this equation: 10x+6=40x, with x being minutes.
So, you have 6=40x-10x=30x. So, x=6/30=1/5.
So, it would take 1/5 minute.
And 1/5 minute = 60*(1/5)seconds = 12 seconds.