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laila [671]
4 years ago
9

Maggie can paint a fence in 9 hours, but Tom needs 12 hours to paint the same fence. How long does it take them to paint the fen

ce if they work together? Round to the nearest tenth.
Mathematics
1 answer:
ehidna [41]4 years ago
4 0

Working together, Maggie and Tom can paint the fence in 5.1 hours

<h3><u>Solution:</u></h3>

Given that,

Maggie can paint a fence in 9 hours

So in 1 hour maggie paints, \frac{1}{9} of the house

Tom needs 12 hours to paint the same fence

So in 1 hour, tom can paint \frac{1}{12} of the house

To find: time taken to paint the fence if they work together

Let "a" be the time taken to paint the fence if they work together

So working together, in 1 hour, they can paint \frac{1}{a} of the house

We can frame a equation as:

To see how much of the fence they can paint together in one hour, we add these together.

\frac{1}{9} + \frac{1}{12} = \frac{1}{a}

\frac{1}{a} is how much of the fence they can paint together in one hour.  Therefore "a" is the number of hours it will take them both to paint the fence

On solving,

\frac{12 + 9}{12 \times 9} = \frac{1}{a}\\\\\frac{1}{a} = \frac{21}{108}\\\\a = \frac{108}{21} = 5.1428

So working together, Maggie and Tom can paint the fence in 5.1 hours

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