SOLUTION: Max can finish repairing a machine in 4 hours. His helper can do the same job in 8 hours. Max began the job alone and work for 2 hours.His helper joined until the job was completed

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Max can finish repairing a machine in 4 hours. His helper can do the same job in 8 hours. Max began the job alone and work for 2 hours.His helper joined until the job was completed      Log On


   

Question 1013760: Max can finish repairing a machine in 4 hours. His helper can do the same job in 8 hours. Max began the job alone and work for 2 hours.His helper joined until the job was completed. How long did it take them to finish the job?
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Two expressions to be summed.
%281%2F4%292%2B%281%2F4%2B1%2F8%29t=1-----total of 1 job, Max for 2 hour and then he and helper for t hours.

Multiply both sides by 8, and then simplify,
4%2B%282%2B1%29t=8
4%2B3t=8
highlight%28t=4%2F3%29

1 hour 40 minutes

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What fraction of the job did Max
get done in 2 hrs?
-------------------
Max's rate of working:
[ 1 machine repaired ] / [ 4 hrs ] = +1%2F4+
Fraction of job done in 2 hrs:
+%28+1%2F4+%29%2A2+=+1%2F2+
-------------------
There is +1+-+1%2F2+=+1%2F2+ of the job left to do
-------------------
Let +t+ = time in hrs for them to finish job working together
Add their rates of working to get their rate working together
+1%2F4+%2B+1%2F8+=+%28%28+1%2F2%29%29+%2F+t+
Multiply both sides by +8t+
+2t+%2B+t+=+4+
+3t+=+4+
+t+=+4%2F3+ hrs
It took them 4/3 hrs = 1 hr and 20 min to finish
the job working together