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,
`(1)/(9)` of the house

Tom needs 12 hours to paint the same fence

So in 1 hour, tom can paint
`(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
`(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.

`(1)/(9) + (1)/(12) = (1)/(a)`

`(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,

`(12 + 9)/(12 * 9) = (1)/(a)\\\\(1)/(a) = (21)/(108)\\\\a = (108)/(21) = 5.1428`

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