Word translation - circular gears

[szDave]

Hello,

Please give me a proper equation for this.

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: 12

[GMATGuruNY]

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 geat P ?
A. 6
B. 8
C. 10
D.12
E.15

When elements COMPETE, calculate the DIFFERENCE between the rates.
Q's rate - P's rate = 40-10 = 30 revolutions per minute.
Implication:
Every minute Q makes 30 more revolutions than P.
Time for Q to make 6 more revolutions = (number of revolutions)/(rate difference) = 6/30 = 1/5 of a minute = 12 seconds.

The correct answer is D.

[Brent@GMATPrepNow]

Hello,

Please give me a proper equation for this.

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: 12

We can solve it using equivalent ratios.
We know that, for every 60 seconds, Q makes 30 more revolutions than P does.
We want to determine how many second it will take Q to make 6 more revolutions than P does.
In our heads, we can see that it will take 1/5 the time (i.e., 12 seconds), but let's use equivalent ratios.

The ratio will be: (# of seconds)/(# of extra revolutions Q makes).
So, we get: 60/30 = x/6
Cross multiply to get 30x = (60)(6)
x = 12
In other words, it will take 12 seconds.

Cheers,
Brent

[rupeshrch]

If you want proper equation and not the quicker solution like above then,
10 rev / min = 1/6 rev per sec.
40 rev/min = 2/3 rev per sec.

Now say after x sec the condition is met, then it means

X*(2/3) = X*(1/6) + 6

4X = X + 36

[sana.noor]

my approach:
rate of p = 1/6 rev per sec
rate of q = 2/3 rev per sec

RT=D
for P--> 1/6 (t) = X rev...t = 6x---1
for Q---> 2/3 rev (t) = X + 6 .....t = (3x + 18)/2-----2

keeping the two equation equal
6x = (3x + 18)/2
solve for x = 2
putting the value of x in either equaion will give you the same answer 12 seconds..