Question

David can paint a fence in ten hours. Alex can paint the same fence in eight hours. If

they worked together how long would it take them?
1/10
1/8
9/40
40/9

Answer 1

40/9

Explanation:

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Answer 2

40/9

Explanation:

Use the work formula,
`(1)/(A)` +
`(1)/(B)` =
`(1)/(T)`, where A is the amount of time it takes one person, B is the amount of time it takes another person, and T is the time it takes for them to work together.

Plug in the times for David and Alex alone:

`(1)/(10)` +
`(1)/(8)` =
`(1)/(T)`

Find the least common denominator, which is 40.

`(4)/(40)` +
`(5)/(40)` =
`(1)/(T)`

`(9)/(40)` =
`(1)/(T)`

Cross multiply and solve for T:

9T = 40

T = 40/9

So, if they worked together, it would take them 40/9 hours