SOLUTION: The workman A finishes the job 2 hours faster than the workman C, and 1 hour slower than workman B. If workman A and B work together the job will be finished in 1 hour and 12 minut

Question 1077702: The workman A finishes the job 2 hours faster than the workman C, and 1 hour slower than workman B. If workman A and B work together the job will be finished in 1 hour and 12 minutes. For how long will all workmen finish the job
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
Time for A to do 1 job, x.

Time for B to do 1 job, x-1.

Time for C to do 1 job, x+2.

-

Workman A and B tegether:

Solve this for x, and then evaluate the one-job times for B and C.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = time in hrs for A to finish the job
= time in hrs for B to finish the job
= time in hrs for C to finish the job
-------------------------------------------
A's rate of working:
[ 1 job ] / [ t hrs ]
B's rate of working:
[ 1 job ] / [ t-1 hrs ]
C's rate of working:
[ 1 job ] / [ t + 2 hrs ]
----------------------
Add the rates for A and B to get
their rate working together

( I coverted minutes to hrs )
Multiply both sides by

Solve with quadratic formula

hrs ( too small, gives negative times )

hrs
hrs
hrs
-------------------------
Add the rates for all three
Let = time in hrs for all three to finish job

Multiply both sides by

hrs
min
min
All 3 working together take 58.06 min
Check the math
( kind of a strange answer )
and get another opinion if possible

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