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Slightly different work problem

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Slightly different work problem

by ellexay » Thu Feb 12, 2009 9:30 am
Here is the problem: J working alone can repair 2 sections of trail in r hrs. K working alone can repair 1 section in p hrs. How long will it take J & K to repair a trail 6 sections long if they work together?





ANS: 6rp/2p+r

HELP! Thank you!

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Re: Slightly different work problem

by Ian Stewart » Thu Feb 12, 2009 9:57 am
ellexay wrote:Here is the problem: J working alone can repair 2 sections of trail in r hrs. K working alone can repair 1 section in p hrs. How long will it take J & K to repair a trail 6 sections long if they work together?

ANS: 6rp/2p+r

HELP! Thank you!
One approach you can take to combined work problems is to calibrate each worker to the same amount of time. It's easier to understand the sequence of steps using a numerical example first:

Say Worker A can complete 2 jobs in 10 hours. How long to complete 1 job? 5 hours --> we divide by 2.

Say worker A can complete 2 jobs in 10 hours. How many jobs will he or she complete in 60 hours? Well, working six times as long, A will do six times the work: we multiply by 6, so A will complete 12 jobs.

We can do the same operations for the above question, though it's more abstract because of the presence of the letters. Still, at each stage, we are simply multiplying or dividing, just as we would do if we were working with numbers. Here, for example, we know:

J can complete 2 jobs in r hours
K can complete 2 job in 2p hours

We can now work out how many jobs they would each do in 2rp hours, by multiplying:

J can complete 4p jobs in 2rp hours
K can complete 2r jobs in 2rp hours
J+K together complete 4p + 2r jobs in 2rp hours

Now divide by 4p + 2r to see how long it takes to complete 1 job:

J+K together complete 1 job in 2rp/(4p + 2r) hours

And finally multiply by 6 to see how long it takes to complete 6 jobs:

J+K together complete 6 jobs in 12rp/(4p + 2r) = 6rp/(2p + r) hours

_______

The combined rate formula could likely also be used here if you know that formula, though if you do as above, you don't need it.
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

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by Stuart@KaplanGMAT » Thu Feb 12, 2009 11:45 am
Excellent explanation as always, Ian!

As you can see, the use of variables instead of numbers is what makes this question particularly tough. If we had been provided with all numbers instead, the reasoning would have been far less abstract.

Accordingly, this would be a great question for picking numbers. Assign values to p and r and then solve the question for those numbers. Then we plug those values into the answer choices and look for our match.

Of course, we can't pick numbers without actually seeing the answer choices, which is why ALL posters should include the full question (plus the source of the question).
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Re: Slightly different work problem

by x2suresh » Thu Feb 12, 2009 11:48 am
ellexay wrote:Here is the problem: J working alone can repair 2 sections of trail in r hrs. K working alone can repair 1 section in p hrs. How long will it take J & K to repair a trail 6 sections long if they work together?





ANS: 6rp/2p+r

HELP! Thank you!
W = R*T

Jrate= w/t = 2/r
Krate = 1/p

combined rate*t = 6
(2/r +1/p) t = 6 --> t= 6rp/(2p+r)

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by ellexay » Thu Feb 12, 2009 1:45 pm
Thank you everyone. I got this source from a non-gmat prep website because I searched for websites that would give me practice in word work problems. The original poster did not have answer choices. =(