Strategy for Multiple Rates Problem

Question

Hi All,
Am relatively new to the forums and have been trolling a bit so thought I'd put up my first question.

Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independantly can process the same number of envelopes in 2 \frac{1}{2}  hours. If machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take machine B to process 12000 envelopes.

2
3
4
6
8

The OA basically crunches the maths and I'm wondering if anyone can offer a strategy which is simpler

shaselai · Answer

i might be interpreting the fraction part wrong (is it 2 and 1/2?) but I got 8.57 for some reason... here what i did:
 A and C working together but ind to proc 3000 in 1 hour. Since A makes 6000 in 3 hours is has rate of 2000/hour so C is 1000/hour.
now for B and C i setup like:
(B+1000)/hr * (5/2 (it's 2 and 1/2?) = 6000 
multiply and divide i got B+1000 = 2400 
B= 1400. so 12000/1400 = 8.5.....

I guess E? not really sure but i think this is probably the right way of doing it?

yangsta8 · Answer

I've fixed the question now but yes it's 2.5.

I just didn't like the idea of crunching it through, the OA explanation was along the lines of what you had.

The way I came up with the answer was:

B + C = 6000 per 2.5 hours
A + C = 3000 per hour = 6000 per 2 hour

So from this I figured A must be faster than B. And since:
A = 6000 per 3 hours = 12000 per 6 hours

Then answer must be > 6. Hence E fits. Just wondering if anyone else had another non number crunching way.

sharkk · Answer

E (i.e. 8.x hrs)

Sorry I don't have a short-cut for solving it.
I solved it step by step in a lengthy way.

bhanushalinikhil · Answer

Well, maths is as simple as you think it is. Heres one way you can solve it. Given A = 6000 env in 3 hours => 2000 in 1 hour. Given B+C = 6000 in 2 and half hours ie 2400 in 1 hour. Given A+C = 3000 in one hour. However, we already know that A is 2000 envelopes per hour. Hence, C must be 1000 envelopes. Therefore, B must be produce 1400 envelopes per hour. Therefore, for 12000 envelopes, approx. 8 and half hours. Hope this helps.

yangsta8 · Answer

Thanks, I guess the mathematical way is quite simple when laid out that way. 
The OA was a little more confusing.

Strategy for Multiple Rates Problem

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