SOLUTION: 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 gra

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

RELATED QUESTIONS
Each of two road graders can pave a certain section of the road in 15 hours working... (answered by stanbon)

Working alone two metal crushers can each process one truckload of aluminum cans in 25... (answered by scott8148)

Two road crews, working together, repaired 1 mile of road in 4 hours. Working separately, (answered by checkley71)

two roads crew working together repaired 1 mile of the road in four hours. working... (answered by ankor@dixie-net.com)

Hi! I've been trying this problem for some time and I can't seem to figure it out. A... (answered by ikleyn,MathTherapy)

A contractor agrees to lay a road 3000m long in 30 days. 50 men are employed and they... (answered by josgarithmetic,ikleyn)

During one week, two machines produce a total of 27 210 parts, with the faster machine... (answered by josgarithmetic)

Two machines fill cereal boxes at the same rate. After the two machines work together... (answered by drk)

a new machine that deposits cement for a road requires 12 hours to complete one-half mile (answered by josgarithmetic)