SOLUTION: Danny and Josh are going to go help paint Josh’s neighbor’s fence. Josh painted the fence by himself two years ago. Four years ago, Danny painted the same fence and did it 9 hours

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Danny and Josh are going to go help paint Josh’s neighbor’s fence. Josh painted the fence by himself two years ago. Four years ago, Danny painted the same fence and did it 9 hours       Log On


   

Question 962771: Danny and Josh are going to go help paint Josh’s neighbor’s fence. Josh painted the fence by himself two years ago. Four years ago, Danny painted the same fence and did it 9 hours faster than Josh. Together, Danny and Josh finished painting the fence in just 7 hours. Show how long it takes for Danny and Josh to paint the fence if they were each doing it by themselves.
Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the time for Josh alone to paint the fence.

PERSON__________RATE
Josh____________1/x
Danny___________1/(x-9)
Josh&Danny______1/7

The rate of both people working together will be the sum of the individual rates.

1%2Fx%2B1%2F%28x-9%29=1%2F7

Use ordinary fraction skills. LCD is 7x%28x-9%29.
Multiply both members by 7x%28x-9%29 and simplify before solving for x.