Rates - Word problem

outty wrote: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?

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One approach is to use equivalent ratios.

We know that, for every 60 seconds, Q makes 30 more revolutions than P does.
We want to determine how many seconds it will take Q to make 6 more revolutions than P does.

We may immediately 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

Hi outty,

This type of Rate question can be answered in a number of different ways (beyond the various "math approaches", you can also TEST THE ANSWERS).

Here's a math approach that isolates each additional rate:

Gear P = 10 revolutions per minute = 1 revolution every 6 seconds
Gear Q = 40 revolutions per minute = 1 revolution every 1.5 seconds

In 6 seconds:
Gear P = 1 revolution
Gear Q = 4 revolutions
Difference = 4 - 1 = Gear Q does 3 MORE revolutions per 6 seconds than Gear P does.

The question asks how long it will take for Gear Q to do 6 MORE revolutions than Gear P, so we double the above result:

6 seconds x 2 = 12 seconds.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Hi outty,

Since I mentioned TESTing THE ANSWERS, here's how that approach would work.

We know the rates of the two gears, so if we were given the amount of time, we COULD figure out the number of revolutions that each Gear made.

Converting the rates into seconds gives us:
Gear P = 10/60 = 1/6 revolution per second
Gear Q = 40/60 = 2/3 revolution per second

Answer B: 8 seconds

In 8 seconds,
Gear P makes 8(1/6) = 1 1/3 revolutions
Gear Q makes 8(2/3) = 5 1/3 revolutions
Difference = 4 revolutions. This is TOO LOW (it's supposed to be exactly 6 revolutions), so we need more time...
Eliminate A and B.

Answer D: 12 seconds

In 12 seconds,
Gear P makes 12(1/6) = 2 revolutions
Gear Q makes 12(2/3) = 8 revolutions
Difference = 6 revolutions. This is EXACTLY what it's supposed to be. We've found the match, so we're done.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich