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?

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

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