SOLUTION: After 5 hours of house painting, Jess asked the assistance of Jon. Together, they finished the job in 4 more hours. Had Jon joined in an hour after Jess started working, the job wo

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Question 324807: After 5 hours of house painting, Jess asked the assistance of Jon. Together, they finished the job in 4 more hours. Had Jon joined in an hour after Jess started working, the job would have been finished in 7 hours. How long would it have taken Jess to paint the house alone?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
After 5 hours of house painting, Jess asked the assistance of Jon.
Together, they finished the job in 4 more hours.
Had Jon joined in an hour after Jess started working, the job would have been finished in 7 hours.
How long would it have taken Jess to paint the house?
:
Let x = Jess time painting the house alone
Let y = Jon's time painting the house
Let the completed job = 1 (a painted house)
:
Write an equation for each scenario
:
"After 5 hours of house painting, Jess asked the assistance of Jon. Together, they finished the job in 4 more hours."
9%2Fx + 4%2Fy = 1
:
"Had Jon joined in an hour after Jess started working, the job would have been finished in 7 hours."
8%2Fx + 7%2Fy = 1
:
We can combine the two equations
9%2Fx + 4%2Fy = 8%2Fx + 7%2Fy
9%2Fx - 8%2Fx = 7%2Fy - 4%2Fy
1%2Fx = 3%2Fy
cross multiply
y = 3x
:
Use substitution in the 1st equation
9%2Fx + 4%2F%283x%29 = 1
multiply by 3x, results
3(9) + 4 = 3x
27 + 4 = 3x
31 = 3x
x = 31%2F3
x = 10.3333 hrs (Jess time alone 101%2F3 hrs)
:
:
check solution, find y
y = 3(10.333)
y = 31 hrs
:
check in the 2nd equation
8%2F10.333 + 7%2F31 =
.714 + .226 = 1, confirms our solution