SOLUTION: jessie and mark are planning to paint a house together. jesse thinks that if he works alone it would take him 5 hours more than the time mark takes to paint the entire house. worki

Algebra ->  Rate-of-work-word-problems -> SOLUTION: jessie and mark are planning to paint a house together. jesse thinks that if he works alone it would take him 5 hours more than the time mark takes to paint the entire house. worki      Log On


   

Question 951539: jessie and mark are planning to paint a house together. jesse thinks that if he works alone it would take him 5 hours more than the time mark takes to paint the entire house. working together, they can complete the job in 6 hours . how would you represent the amount of work that mark can finish in 1 hour ?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Jessie and mark are planning to paint a house together.
Jesse thinks that if he works alone, it would take him 5 hours more than the time mark takes to paint the entire house.
working together, they can complete the job in 6 hours .
how would you represent the amount of work that mark can finish in 1 hour ?
:
let m = time required by Mark to paint the house
It takes Jessie 5 hrs longer, therefore
(m+5) = time required by Jessie to paint the house
let the completed job = 1 (a painted house)
A shared work equation
6%2Fm + 6%2F%28%28m%2B5%29%29 = 1
Multiply by m(m+5), cancel the denominators and you have
6(m+5) + 6m = m(m+5)
6m + 30 + 6m = m^2 + 5m
12m + 30 = m^2 + 5m
Form a quadratic equation on the right
0 = m^2 + 5m - 12m - 30
m^2 - 7m - 30 = 0
Factors to
(m-10)(m+3) = 0
the postive solution is what we want here
m = 10 hrs for Mark to paint the house by himself
:
"how would you represent the amount of work that mark can finish in 1 hour"
He could paint 1%2F10 of the house in 1 hr.