SOLUTION: MACHINE A TAKES 36 HOURS TO DO A JOB THAT MACHINE B DOES IN 24 HOURS.IF MACHINE RUNS FOR 12 HRS. BEFORE MACHINE B IS TURNED ON, HOW LONG WILL IT TAKE BOTH MACHINES RUNNING TOGETHER

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Question 375974: MACHINE A TAKES 36 HOURS TO DO A JOB THAT MACHINE B DOES IN 24 HOURS.IF MACHINE RUNS FOR 12 HRS. BEFORE MACHINE B IS TURNED ON, HOW LONG WILL IT TAKE BOTH MACHINES RUNNING TOGETHER TO FINISH THE JOB IF THEY WORK TOGETHER?
Answer by nerdybill(7384) About Me  (Show Source):
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MACHINE A TAKES 36 HOURS TO DO A JOB THAT MACHINE B DOES IN 24 HOURS.IF MACHINE RUNS FOR 12 HRS. BEFORE MACHINE B IS TURNED ON, HOW LONG WILL IT TAKE BOTH MACHINES RUNNING TOGETHER TO FINISH THE JOB IF THEY WORK TOGETHER?
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Since mach A ran for 12 hours, the portion of the job done is:
12(1/36) = 12/36 = 1/3 of the job completed before mach B starts
.
Let x = time (hrs) for mach A/B to complete job
then
x(1/36 + 1/24) = 1 - 1/3
x(1/36 + 1/24) = 3/3 - 1/3
x(1/36 + 1/24) = 2/3
multiplying both sides by 3:
x(1/12 + 1/8) = 2
multiplying both sides by 24:
x(2 + 3) = 48
x(5) = 48
x = 48/5
x = 9.6 hours
or
x = 9 hours and 36 minutes