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

Algebra ->  Rate-of-work-word-problems -> 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      Log On


   

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) About Me  (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:
1%2Fx%2B1%2F%28x-1%29=1%2612%2F60
Solve this for x, and then evaluate the one-job times for B and C.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs for A to finish the job
+t+-+1+ = time in hrs for B to finish the job
+t+%2B+2+ = 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
+1%2Ft+%2B+1%2F%28+t-1+%29+=+1%2F1.2+
( I coverted minutes to hrs )
Multiply both sides by +t%2A%28+t-1+%29%2A1.2+
+1.2%2A%28+t-1+%29+%2B+1.2t+=+t%2A%28+t-1+%29+
+1.2t+-+1.2+%2B+1.2t+=+t%5E2+-+t+
+t%5E2+-+3.4t+%2B+1.2+=+0+
+10t%5E2+-+34t+%2B+12+=+0+
+5t%5E2+-+17t+%2B+6+=+0+
Solve with quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+5+
+b+=+-17+
+c+=+6+
+t+=+%28-%28-17%29+%2B-+sqrt%28+%28-17%29%5E2-4%2A5%2A6+%29%29%2F%282%2A5%29+
+t+=+%28+17+%2B-+sqrt%28+289-120+%29%29%2F+10+
+t+=+%28+17+%2B-+sqrt%28+169+%29%29%2F+10+
+t+=+%28+17+-+13+%29+%2F+10+
+t+=+.4+ hrs ( too small, gives negative times )
+t+=+%28+17+%2B+13+%29%2F10+
+t+=+3+ hrs
+t+-1+=+2+ hrs
+t+%2B+2+=+5+ hrs
-------------------------
Add the rates for all three
Let +T+ = time in hrs for all three to finish job
+1%2Ft+%2B+1%2F%28+t-1+%29+%2B+1%2F%28+t%2B2+%29+=+1%2FT+
+1%2F3+%2B+1%2F2+%2B+1%2F5+=+1%2FT+
Multiply both sides by +30T+
+10T+%2B+15T+%2B+6T+=+30+
+31T+=+30+
+T+=+.96774+ hrs
+T+=+.96774%2A60+ min
+T+=+58.06+ min
All 3 working together take 58.06 min
Check the math
( kind of a strange answer )
and get another opinion if possible