SOLUTION: Dear... A finishes a paint job in two hours less than B. C paints as quickly as A and B together. They need to paint a room. C is late. After an hour of painting, C shows up. All

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Dear... A finishes a paint job in two hours less than B. C paints as quickly as A and B together. They need to paint a room. C is late. After an hour of painting, C shows up. All      Log On


   

Question 1073802: Dear...
A finishes a paint job in two hours less than B. C paints as quickly as A and B together. They need to paint a room. C is late. After an hour of painting, C shows up. All three together finish the job 3 and a half hours later, How long did take each painter to paint the room?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
PAINTER       RATE

A            1%2F%28x-2%29

B            1%2Fx

C            1%2F%28x-2%29%2B1%2Fx


A and B paint for 1 hour;
A, B, and C paint for 3.5 hours, and the one whole job is finished.

A and B for 1 hour:
%281%2F%28x-2%29%2B1%2Fx%29%2A1

A, B, and C for 3.5 hours:
%281%2F%28x-2%29%2B1%2Fx%29%2A%283.5%29%2B%281%2F%28x-2%29%2B1%2Fx%29%2A%283.5%29

The SUM of those two expressions is 1
for ONE WHOLE PAINT JOB.

Set up the sum, solve for x, and then evaluate the time for each of A and C to do one job if alone. (or, their rates).