bml1105 wrote:Machine A and Machine B are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than Machine B. Machine B produces 10% more sprockets per hour than Machine A. How many sprockets per hour does machine A produce?

(A) 6
(B) 6.6
(C) 60
(D) 100
(E) 110

We can PLUG IN THE ANSWERS, which represent A's rate.
It is stated that B produces 10% more sprockets per hour than A.
Thus, when the correct answer choice is plugged in, B's rate will be 110% of A's rate.

The answer choices imply the following times for A:
660/6 = 110 hours.
660/6.6 = 100 hours.
660/60 = 11 hours.
660/100 = 6.6 hours.
660/110 = 6 hours.

It is stated that A's time is 10 hours longer than B's time.
Thus:
Answer choices D and E are not possible.
Answer choice C seems unlikely, since it implies that B's time is 1 hour.
Answer choice B implies that B's time = 90, a value that does not divide easily into 660.
The correct answer almost certainly is A.

Answer choice A: A's rate = 6 sprockets per hour
Since A's time of 110 hours is 10 hours longer than B's time, B's time = 100 hours.
Thus, B's rate = 660/100 = 6.6 sprockets per hour.
(B's rate)/(A's rate) = 6.6/6 = 11/10 = 110%.
Success!

The correct answer is A.

bml1105 wrote:Machine A and Machine B are each used to manufacture 660 sprockets. It takes maching A 10 hours longer to produce 660 sprockets than Machine B. Machine B produces 10% more sprockets per hour than Machine A. How many sprockets per hour does machine A produce?

(A) 6
(B) 6.6
(C) 60
(D) 100
(E) 110

OA: A

Alternate approach:

Since B produces 10% more sprockets per hour than A, for every 10 sprockets produced by A, B produces 11 sprockets.
Thus, the RATE RATIO for A and B = 10:11.
Since rate and time are reciprocals, the TIME RATIO for A and B = 11:10.
Since A's time is 10 hours longer than B's time, and 11:10 = 110:100, A's time = 110 hours, while B's time = 100 hours.
Thus, A's rate = w/t = 660/110 = 6 sprockets per hour.

The correct answer is A.

So the best way to answer this question really is just plugging in numbers or answer choices?

I kept trying to make it work with just equations, and I couldn't make it work.

bml1105 wrote:So the best way to answer this question really is just plugging in numbers or answer choices?

I kept trying to make it work with just equations, and I couldn't make it work.

Here's an algebraic solution:

Let A = A's rate.
Since B produces 10% more sprockets per hour, B's rate = 1.1A.

A's time = w/r = 660/A.
B's time = w/r = 660/1.1A = 600/A.
Since A's time is 10 hours longer than B's time, we get:
660/A = 600/A + 10
60/A = 10
60 = 10A
A = 6.

The correct answer is A.