# Working alone, it takes Maria nine hours to dig a 10 ft by 10 ft hole. Darryl can dig the same hole in ten hours. How long would it take them if they worked together?

Jul 4, 2018

$4.7368421052631575 \setminus \textrm{h r s}$

#### Explanation:

Maria alone takes $9$hrs to dig a hole hence one hour work of Maria

$= \frac{1}{9}$

Darryl alone takes $10$hrs to dig the same hole hence one hour work of Darryl

$= \frac{1}{10}$

Now, the fraction of work done in one hour by Maria & Darryl working together

$= \frac{1}{9} + \frac{1}{10}$

If takes total $h$ hrs for Maria & Darryl working together to complete the same work then

$h \left(\frac{1}{9} + \frac{1}{10}\right) = 1$

$h = \frac{1}{\frac{1}{9} + \frac{1}{10}}$

$= \frac{1}{\frac{19}{90}}$

$= \frac{90}{19}$

$= 4.7368421052631575 \setminus \textrm{h r s}$