SOLUTION: Anthony and Donita can complete a project in 21/5 hours. It takes Donita 14 hours to do the same project working alone. How long does it take Anthony to complete the project when h

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Anthony and Donita can complete a project in 21/5 hours. It takes Donita 14 hours to do the same project working alone. How long does it take Anthony to complete the project when h      Log On


   

Question 211416: Anthony and Donita can complete a project in 21/5 hours. It takes Donita 14 hours to do the same project working alone. How long does it take Anthony to complete the project when he works alone?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let A = time it takes Anthony to do the job alone
D= time for Donita to do the job alone = 14 hours
T= time for Anthony and Donita to do the job together= 21/5 hours

The basic equation is 1%2FA+%2B+1%2FD+=+1%2FT
1%2FA+%2B+1%2F14=1%2F%2821%2F5%29
1%2FA+%2B+1%2F14+=+5%2F21

The LCD for the equation is actually 7*2*3*A = 42A, so multiply both sides of the equation by 42A.

42A%2A%281%2FA%29%2B+42A%2A%281%2F14%29+=+42A%2A%285%2F21%29+
42+%2B+3A+=+10A+
42+=+7A+
6+=+A

Anthony will take 6 hours to complete the project alone.

R^2

Dr. Robert J. Rapalje, Retired