SOLUTION: Eric and Ryan have been hired to paint the houses in a new development. Working together the men can paint the house in two-thirds the time that it takes eric working alone. Ryan t

Question 930639: Eric and Ryan have been hired to paint the houses in a new development. Working together the men can paint the house in two-thirds the time that it takes eric working alone. Ryan takes six hours to paint a house alone. How long does it take eric to paint a house working alone?
Found 3 solutions by ewatrrr, Alan3354, TimothyLamb:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
x time it takes Eric alone
Per hr the KEY

|Multiplying thru by 12x so as all denominators = 1
2x + 12 = 18
2x = 6
x = 3, time it takes Eric alone
and..checking
1/6 + 1/3 = 1/6 + 2/6 = 1/2
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Eric and Ryan have been hired to pain the houses in a new development. Working together the men can paint the house in two-thirds the time that it takes eric working alone. Ryan takes six hours to paint a house alone. How long does it take eric to paint a house working alone?
==============
It takes Eric E hours, take Ryan R hours (each working alone)
Eric does 1/E per hour, Ryan does 1/R per hour.
R = 6 hours
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They do (1/E + 1/6) = (E + 6)/6E job/hour together
--> 6E/(E + 6) hours/job together
6E/(E + 6) = (2/3)E
6/(E + 6) = (2/3)
2(E + 6) = 18
E = 3 hours
Answer by TimothyLamb(4379)   (Show Source): You can put this solution on YOUR website!
x = time eric alone takes to paint
y = time ryan alone takes to paint = 6 hours
z = time eric and ryan together take to paint = (2/3)x
---
r = w/t
rates are additive:
---
eric rate = 1/x
---
ryan rate = 1/6
---
together rate:
1/x + 1/6 = 1/z
1/x + 1/6 = 1/(2/3)x
1/x - 1/(2/3)x = -1/6
(2/3)/(2/3)x - 1/(2/3)x = -1/6
(2/3) - 1 = (-1/6)*(2/3)x
(2/3) - (3/3) = (-1/6)*(2/3)x
-(1/3) = (-1/6)*(2/3)x
x = -(1/3)/( (-1/6)*(2/3) )
x = 3
---
answer:
x = time eric alone takes to paint = 3 hours
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