Question 394216: Evan, John, and Mark are on the same Learning Team at UOP. If each worked on the team assignments alone, it would take Evan 10 hours, John 8 hours, and Mark 12 hours to finish the assignments. They usually started the same time on Monday night after work. But last week, Evan started early and he worked for 2 hours on the assignments when John and Mark began. Later, all three finished the team assignments. How long did they take to finish by working together?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Evan, John, and Mark are on the same Learning Team at UOP. If each worked on the team assignments alone, it would take Evan 10 hours, John 8 hours, and Mark 12 hours to finish the assignments.
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They usually started the same time on Monday night after work. But last week, Evan started early and he worked for 2 hours on the assignments when John and Mark began. Later, all three finished the team assignments. How long did they take to finish by working together?
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Evan rate: 1/10 job/hr
John rate: 1/8 job/hr
Mark rate: 1/12 job/hr
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Evan finished 2/10 of the job in 2 hrs.
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Equation:
Let "x" be time to finish the job together:
x[1/10+1/8+1/12] = 8/10 job
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x[(12 + 15 + 10)/120] = 8/10
x[37/120] = 8/10
x = (120/37)(8/10)
x = (12*8/37)
x = 2.59 hrs
x = 2 hr 35min 24sec
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Cheers,
Stan H.
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