Question 68586
Working together on a job Patrick by himself can paint four rooms in 10 hours. if he hires April to help they can do the same job together in 6 hours. if he lets April work alone how long will it take her to paint 4 rooms.
:
Let t = time required by April to do it alone: Let the completed job = 1 
:
{{{6/10 + 6/t}}} = 1
:
Multiply the equation by 10t to get rid of the denominators:
6t + 10(6) = 10t
:
6t + 60 = 10t
:
6t - 10t = -60
:
-4t = -60
:
t = -60/-4
:
t = +15 hrs for A to paint the 4 rooms alone
:
:
Check:
{{{6/10 + 6/15}}} = 1
:
Did this make sense to you?