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
b working alone 1 T+1
c working alone 1 2T
all 3 working together 1 T
The equation comes from:
+ + =
+ + =
Solve that equation and get T = of an hour or 40 minutes.
Edwin