Question

Faith and Katie are working together to repair a fence. Together they can fix it in 10 hours. Alone faith takes 22 hours to complete, how long does it take katie

Answer 1

The time taken by Katie alone to repair the fence is 18.3 hours

Explanation:

Given as :

Faith and Katie are working together to repair a fence

The time taken by both to fix it = 10 hours

The time taken by Faith alone to fix it = 22 hours

Let The time taken by Katie alone to fix it = T hours

Now, According to question

The time taken by both to fix it = The time taken by Faith alone to fix it + The time taken by Katie alone to fix it

Or ,
`(1)/(10)` =
`(1)/(22)` +
`(1)/(T)`

Or,
`(1)/(T)` =
`(1)/(10)` -
`(1)/(22)`

Taking LCM

Or,
`(1)/(T)` =
`(11 - 5)/(110)`

Or,
`(1)/(T)` =
`(6)/(110)`

∴ T =
`(110)/(6)`

or, T =
`(55)/(3)`

I.e T = 18.3 hours

So,The time taken by Katie alone to fix it = T = 18.3 hours

Hence,The time taken by Katie alone to repair the fence is 18.3 hours Answer