SOLUTION: Machine A can do a job alone in 10 hours. Machine B can do the same job alone in 12 hours. Machine A is turned on at 6am Machine B is turned on at 9 a.m. Machine A breaks down at 1
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Question 1189402: Machine A can do a job alone in 10 hours. Machine B can do the same job alone in 12 hours. Machine A is turned on at 6am Machine B is turned on at 9 a.m. Machine A breaks down at 10 a.m., and Machine B must finish the job alone. When will Machine B finish? Found 3 solutions by Boreal, ikleyn, math_tutor2020:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! in 1 hour A can do 1/10 the job and B can do 1/12 the job.
At 10 am, A has been on the job 4 hours and has done 4/10. B has been on 1 hour and has done (1/12)
So the amount left to do is 1-(24/60)-(5/60) or 31/60
31/60/1/12=(31/60)*12=6.2 hours
10 am +6.2 hours is 4:12 pm
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4 hours of A (4/10)
7.2 hours of B (7.2/12)
Machine A worked 4 hours and completed 4/10 of the job. 6/10 of the job left.
Machine B completed remaining 6/10 of the job in = = 7.2 hours = 7 hours and 12 minutes.
Since machine B started at 9 am, it completed the job at 4:12 pm. ANSWER
Machine A can inspect 60 items in 10 hours. Its unit rate is 60/10 = 6 items per hour.
Machine B can inspect 60 items in 12 hours. Its unit rate is 60/12 = 5 items per hour.
Machine A runs from 6 AM to 10 AM, which is a duration of 4 hours. Over this timespan, the machine inspects 6*4 = 24 items.
This leaves 60-24 = 36 items for Machine B to inspect.
Machine B can inspect 5 items per hour, and must inspect 36 of them. That means it needs 36/5 = 7.2 hours
When dividing the number of items over the unit rate, the "items" unit cancels leaving just the hours.
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