SOLUTION: A can do a piece of work in 18 days and B can do it in 21 days. A, B, and C together can finish the work in 7 days. How long will it take C alone to finish the work?
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Question 198523: A can do a piece of work in 18 days and B can do it in 21 days. A, B, and C together can finish the work in 7 days. How long will it take C alone to finish the work? Answer by Edwin McCravy(20054) (Show Source):
You can put this solution on YOUR website! A can do a piece of work in 18 days and B can do it in 21 days. A, B, and C together can finish the work in 7 days. How long will it take C alone to finish the work?
Let x be the number of days C to finish the work.
Make this chart, filling in 1's for the number of pieces of work,
since exactly 1 was done in each case. Then fill in the given
times and the unknown time x for C
PIECES OF WORK = RATE * TIME
A 1 18
B 1 21
C 1 x
----------------------------------------
A&B&C 1 7
Now we fill in the rates in pieces of work per day,
using
PIECES OF WORK = RATE * TIME
A 1 1/18 18
B 1 1/21 21
C 1 1/x x
----------------------------------------
A&B&C 1 1/7 7
So we add up the rates of A, B, and C and that must equal
to their combined rate. We get it all from the middle
column:
Can you solve that for x? Answer: days.
Edwin
