SOLUTION: Please help me solve this problem. A physics professor can perform an experiment two times as fast as her graduate assistant. The professor left after 4 hours of working together

Question 335833: Please help me solve this problem.
A physics professor can perform an experiment two times as fast as her graduate assistant. The professor left after 4 hours of working together to attend a meeting while the assistant worked 2 more hours ti finish the experiment. How long would it take each of them working alone?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
If x is the rate of the graduate assistance, then 2*x is the rate of the professor.

The total time the project took was 6 hours.

4 of those hours was working together and 2 or those hours was the assistant working alone.

Since rate * time = units produced, the formula for the completion of the project is therefore:

4 * (2*x + x) + 2*x = 1, where 1 is the units produced (the project is 1 unit).

Their combined rate is (2*x + x).

the assistant's rate, working alone, is x.

We need to solve for x.

Simplify the formula to get:

4 * (3*x) + 2*x = 1 which becomes:

14*x = 1 which means that:

x = 1/14.

That's the rate of the assistant.

the rate of the professor is 2 times that = 2/14.

To test this out, we plug (1/14) for the rate of the assistant and (2/14) for the rate of the professor in the original equation to get:

4 * (3/14) + 2 * (1/14) = 12/14 + 2/14 = 1.

The question was, how long it would take for each to complete the project alone?

Our unknown variable now becomes time, which we'll call T.

The professor, working alone, would complete the project using the following formula:

(2/14) * T = 1

Solve for T to get T = 7 hours.

The assistant to the professor, working alone, would complete the project using the following formula:

(1/14) * T = 1

Solve for T to get T = 14 hours.

It would take the professor, working alone, 7 hours to complete the project.

It would take the assistant to the professor, working alone, 14 hours to complete the project.

If they both worked the project together to completion, it would take them:

(2/14 + 1/14) * T = 1 which becomes (3/14) * T = 1.

Solve for T to get 4.66666666667 hours which equates to 4 and 2/3 hours.

You didn't need that last bit of trivia, but I just threw it in for good measure.

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