SOLUTION: Joe and Moe can mow the lawn in 32 minutes if they work together. If Moe works twice as fast as Joe, how long does it take Joe to mow the lawn alone?

Question 1125097: Joe and Moe can mow the lawn in 32 minutes if they work together. If Moe works twice as fast as Joe, how long does it take Joe to mow the lawn alone?

Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Joe, rate of r
Moe, rate of 2r
Rate as LAWNS per MINUTE

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96 minutes for Joe to mow the lawn himself.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

When Joe and Moe work together, it is the same as if THREE instances of Joe work simultaneously: Joe1, Joe2 and Joe3. The condition informs us that these tree instances of Joe will complete the job in 32 minutes; it means that Joe alone will do the entire job in 3*32 = 96 minutes, which answers the question.

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So, it is the way to solve the problem MENTALLY, without using equations.

Formally, it is the same logic as in the solution by @josgarithmetic, but presented in wording form without using equations.

It would be ideally if you, the reader (the student) have both these technologies (methods) in your hands and in your mind.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

I strongly agree with tutor @ikleyn that you should be able to solve a problem like this with logical analysis, without algebra.

Here is a solution by logical reasoning that takes a somewhat different path than hers.

If Moe works twice as fast as Joe, then when working together Moe does 2/3 of the job while Joe does 1/3.

That means Joe does 1/3 of the job in 32 minutes; and that means it would take him 3*32 = 96 minutes to do the whole job alone.
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