Question

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 fence if they work together? Round to the nearest tenth.

Answer 1

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

Solution:

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