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Question 300639: Each of two road graders can smooth a section of road in 10 hours working alone. After the two machines have been working for exactly one hour they are joined by an older model grader that would take 12 hours to somooth the section of road by itself. If the first two graders started working on the section of road at 8:00 a.m., at what time of the day (to the the nearest minute) will the section of road be completed?
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Each of two road graders can smooth a section of road in 10 hours working alone. After the two machines have been working for exactly one hour they are joined by an older model grader that would take 12 hours to somooth the section of road by itself. If the first two graders started working on the section of road at 8:00 a.m., at what time of the day (to the the nearest minute) will the section of road be completed?
each of the road graders finish the job in 10 hours alone
each machine completes 1/10 of the job in 1 hour
two machines will do 2/10 of the job in 1 hour.
the third machine takes 12 hours to do the job alone
so it can do 1/12 of the job in 1 hour
when it joins the two other machines have completed 2/10 of the job already.
Balance job when third machine joins = 1-2/10 = 4/5
All three will do 1/10 + 1/10 +1/12 of the job in 1 hour = 34/120 of the job
34/120 of the job they do in 1 hour
so 4/5 of the job they will do in how many hours
4/5 / 34/120
4/5 * 120 /34
2*24 / 17
48 /17 hours
48 / 17
2 hours and 49 minutes
They will complete the job at 10.49 AM
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