Problem Solving

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?

6
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10
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15

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

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?

6
8
10
12
15

Here's another approach:

First rewrite speeds as revolutions per second (since the question uses these units)

Gear P makes 10 revolution per minute, in other words 10 revolutions per 60 seconds.
To determine the number of revolutions per 1 second, divide 10 by 60, to get 10/60 revolutions per second (a.k.a. 1/6 revolutions per second)

Gear Q makes 40 revolution per minute (or 40 revolutions per 60 seconds).
To determine the number of revolutions per 1 second, divide 40 by 60, to get 40/60 revolutions per second (a.k.a. 2/3 revolutions per second)

Now let t = the time in seconds

The number of revolutions gear P makes in t seconds = (1/6)t
The number of revolutions gear Q makes in t seconds = (2/3)t

We need to determine the number of seconds it takes such that gear Q makes exactly 6 more revolutions than gear P.

So, we want to know the value of t such that:
(Q's revolutions) - (P's revolutions) = 6
Or . . . (2/3)t - (1/6)t = 6
To solve, first multiply both sides by 6 to get: 4t - t = 36
3t = 36
t = 12

It will take 12 seconds, so the answer is D

Cheers,
Brent

Hi didieravoaka,

Once you convert each rate into revolutions/second, TESTing THE ANSWERS is a remarkably easy way to get to the correct answer.

Algebraically, you can treat it as a "combined rate" question though:

Distance = (Rate) x (Time)

6 revolutions = (difference in rates) x (Time)

6 revolutions = (30 revolutions/min) x (Time)

6/30 = Time in minutes

1/5 minute = Time

Since the question asks for an answer in SECONDS, we have to convert....

1/5 minute = 12 seconds

Final Answer: D

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

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?

6
8
10
12
15

As we can see, Gear Q makes 30 more revolutions per minute than Gear P does. So, we can set up the following proportion to solve for the number of seconds for Gear Q to make 6 more revolutions than Gear P does:

30 revolutions/1 minute = 6 revolutions/x seconds

We need the units of time to be the same in the denominator. Since 1 minute = 60 seconds, we can say:

30/60 = 6/x

Cross multiply and we have:

30x = 360

x = 12

Answer: D