SOLUTION: A can do certain task in 8 hours, B in 10 hours and C in 12 hours. How long will it take to do the task if A and B work 1 hour and then A and C finish the task?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A can do certain task in 8 hours, B in 10 hours and C in 12 hours. How long will it take to do the task if A and B work 1 hour and then A and C finish the task?      Log On


   

Question 1103606: A can do certain task in 8 hours, B in 10 hours and C in 12 hours. How long will it take to do the task if A and B work 1 hour and then A and C finish the task?
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
Rate of work of A is 1%2F8 of the job per hour; of B is 1%2F10 and of C 1%2F12 of the job per hour.

When A and B worked together for 1 hour, they completed 1%2F8%2B1%2F10 = 5%2F40+%2B+4%2F40 = 9%2F40 of the job.

Hence, 1-9%2F40 = 31%2F40 of the work remained uncompleted.


The combined rate of work for B and C is 1%2F10%2B1%2F12 = 6%2F60%2B5%2F60 = 11%2F60.


So, the answer to the problem question is this ratio  %28%2831%2F40%29%29%2F%28%2811%2F60%29%29 = %2831%2A60%29%2F%2811%2A40%29 = %2831%2A3%29%2F%2811%2A2%29 = 93%2F22 hours = 45%2F22 hours.