SOLUTION: A and B can do a piece of work in 6 days, B and C can do it in 10 days and C and A do it in 15 days. (a) In how many days will A, B and C finish it working together? (b) In how

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A and B can do a piece of work in 6 days, B and C can do it in 10 days and C and A do it in 15 days. (a) In how many days will A, B and C finish it working together? (b) In how       Log On


   

Question 828568: A and B can do a piece of work in 6 days, B and C can do it in 10 days and C and A do it in 15 days.
(a) In how many days will A, B and C finish it working together?
(b) In how many days will A and B finish their working alone?
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
To start, form all the stated rates as "piece of work per day".

A&B: 1/6
B&C: 1/10
C&A: 1/15

The rates of any combination of these workers is the sum of the rate of the workers in the combination of workers.

Looking at the combinations given, find that C&A rate is missing the rate of B. Looking at A&B, and B&C, If you put these rates together, you find B occurs two times. A&B+B&C-2B=C&A. Putting that into the numeric information which corresponds, 1%2F6%2B1%2F10-2B=1%2F15, permitting to find the rate for B if working alone.

Handle similarly with the other two individual rates.
B&C+C&A-2C=A&B
1%2F10%2B1%2F15-2C=1%2F6-----Solve for C.
'
C&A+A&B-2A=B&C
1%2F15%2B1%2F6-2A=1%2F10----Solve for A.

Each of the three equations gives the rate for the single unknown rate depending on whose rate is the unknown variable.