SOLUTION: I need to do the following problem: A carpenter and his partner can put up a patio cover in 3 3/7 hours. If the partner needs 8 hours to complete the cover alone, how long would i

Algebra ->  Rate-of-work-word-problems -> SOLUTION: I need to do the following problem: A carpenter and his partner can put up a patio cover in 3 3/7 hours. If the partner needs 8 hours to complete the cover alone, how long would i      Log On


   

Question 692265: I need to do the following problem: A carpenter and his partner can put up a patio cover in 3 3/7 hours. If the partner needs 8 hours to complete the cover alone, how long would it take the carpenter working alone? I must show my work.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=the amount of time it takes the carpenter working alone to put up the cover
Then the carpenter works at the rate of 1/x of the cover per hour
The carpenter and his partner works at the rate of 1/(3 3/7)=1/(24/7)=7/24 of the cover per hour
The partner works at the rate of 1/8 of the cover per hour, soooo
1/x + 1/8 =7/24 multiply each term by 24x
24+3x=7x
4x=24
x=6 hours time it takes the carpenter working alone
CK
1/6+1/8=7/24
4/24+3/24=7/24
7/24=7/24
Hope this helps---ptaylor