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

Answer:

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

Step-by-step 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 , $\dfrac{1}{10}$ = $\dfrac{1}{22}$ + $\dfrac{1}{T}$

Or,  $\dfrac{1}{T}$ = $\dfrac{1}{10}$ - $\dfrac{1}{22}$

Taking LCM

Or, $\dfrac{1}{T}$ = $\dfrac{11 - 5}{110}$

Or, $\dfrac{1}{T}$ = $\dfrac{6}{110}$

∴ T = $\dfrac{110}{6}$

or, T = $\dfrac{55}{3}$

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