SOLUTION: Three friends a,b,c can do a piece of work in T hours working together. working alone, a can do the work in 6 hours more, b in 1 hour more and c in twice the time if all of them we

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Three friends a,b,c can do a piece of work in T hours working together. working alone, a can do the work in 6 hours more, b in 1 hour more and c in twice the time if all of them we      Log On


   

Question 551064: Three friends a,b,c can do a piece of work in T hours working together. working alone, a can do the work in 6 hours more, b in 1 hour more and c in twice the time if all of them were working together. How long would it take to finish the work if all of them were working together (find the value of T)?
Answer by AnlytcPhil(1810) About Me  (Show Source):
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Three friends a,b,c can do a piece of work in T hours working together. working alone, a can do the work in 6 hours more, b in 1 hour more and c in twice the time if all of them were working together. How long would it take to finish the work if all of them were working together (find the value of T)?
Make this chart.

                        number of      number of    time in            
                        pieces of        hours      pieces of
                          work         required     work/hour
a working alone

b working alone

c working alone

all 3 working together 

In each case exactly 1 piece of work is completed, so we put 
1 for the number of pieces of work in all 4 cases.  We also put
in T for the time for all three working together, T+6 hours for 
a's time, T+1 hours for b's time, and 2T for c's time.

                        number of      number of     rate in            
                        pieces of        hours      pieces of
                          work         required     work/hour
a working alone             1             T+6

b working alone             1             T+1

c working alone             1              2T

all 3 working together      1              T

We fill in the rates in pieces of work/hour by dividing the
number of pieces of work by the hours required:

                        number of      number of     rate in            
                        pieces of        hours      pieces of
                          work         required     work/hour
a working alone             1             T+6        1%2F%28T%2B6%29
b working alone             1             T+1        1%2F%28T%2B1%29
c working alone             1              2T        1%2F%282T%29 
all 3 working together      1              T          1%2FT

The equation comes from:

       %28matrix%284%2C1%2C%22a%27s%22%2Crate%2Cworking%2Calone%29%29 + %28matrix%284%2C1%2C%22b%27s%22%2Crate%2Cworking%2Calone%29%29 + %28matrix%284%2C1%2C%22c%27s%22%2Crate%2Cworking%2Calone%29%29 = %28matrix%286%2C1%2C+++%0D%0A%0D%0Arate%2C+of%2C+all%2C+three%2C+working%2C+together%29%29 

             1%2F%28T%2B6%29 + 1%2F%28T%2B1%29 + 1%2F%282T%29 = 1%2FT


Solve that equation and get T = 2%2F3 of an hour or 40 minutes.

Edwin