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?

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Answer 1 · 2018-07-04T09:05:59

$4.7368421052631575\ text{hrs}$

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

$=1/9$

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

$=1/10$

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

$=1/9+1/10$

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

$h(1/9+1/10)=1$

$h=1/(1/9+1/10)$

$=1/(19/90)$

$=90/19$

$=4.7368421052631575\ text{hrs}$