Explain this math problem please???

[summertime]

The water from one outlet flowing at a constant rate can fill a swimming pool at 9 hours and from a second out at 5 hours.

If both outlets are used at the same time, what is the number of hours required to fill the pool.

I figured out:

1/9 + 1/5 = 14/45 or .31 however in the book the answer is

45/14 or 3.21.

Can someone explain why did they take the inverse of 14/45 to make the answer 45/14?

[Ian Stewart]

The water from one outlet flowing at a constant rate can fill a swimming pool at 9 hours and from a second out at 5 hours.

If both outlets are used at the same time, what is the number of hours required to fill the pool.

I figured out:

1/9 + 1/5 = 14/45 or .31 however in the book the answer is

45/14 or 3.21.

Can someone explain why did they take the inverse of 14/45 to make the answer 45/14?

Remember in the version of the combined rates formula you're using above, the right hand side of the formula is 1/T, and not T. That is, the formula is:

(1/A) + (1/B) = 1/T

So when you solved, and got 14/45, that was equal to 1/T. To find T, you need to take the reciprocal; T = 45/14, which is a bit bigger than 3.

[anujan007]

Is there any other way of approaching the solution? I mean is it absolutely necessary to go to the 1/T formula? Cant we just eliminate the answers?

The approach I used is of taking a quick look at the answers. C is 2.5. In 2.5 hours the second inlet fills the half tank (5/2) but the first needs atleast 4.5 (9/2) to fill half the tank. Eliminate C.

So it has to be more than 2.5 hours. Taking E it is 4.5 hours. Using above logic it surely means that the tank will overflow when both inlets work together for 4.5.

This leaves us with the answer choice D as the correct one.

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Is this approach not the faster way of doing it?