SOLUTION: If one professional roofer can roof and house in six days and another roofer can do it in 4 days how long does it take to roof the house together?

Question 270124: If one professional roofer can roof and house in six days and another roofer can do it in 4 days how long does it take to roof the house together?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time needed if both roofers work together
So, together the two roofers work at the rate of 1/x roof per day
The first roofer works at the rate of 1/6 roof per day
The other roofer works at the rate of 1/4 roof per day
Our equation to solve, then is:
1/6 + 1/4 = 1/x multiply each term by 12x
2x+3x=12
5x=12
x=2.4 days------------------time needed when both are working together
CK
In 2.4 days, first roofer completes (2.4)/6 of the roof
In 2.4 days the other roofer completes (2.4)/4 of the roof
(2.4)/6 + (2.4)/4 should add up to 1 (1 roof, that is)
(4.8)/12 +(7.2)/12=12/12 or 1
1=1

Hope this helps---ptaylor
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