Andrew M. answered • 01/29/16
Tutor
New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
Let M = Marcus time alone
Let C = Claudia's time alone
2.09(1/M + 1/C) = 100%
2.09(1/3.15 + 1/C) = 1
1/3.15 + 1/C = 1/2.09
1/C = 1/2.09 - 1/3.15
1/C = 0.161
C = 1/.161
C = 6.21 hours
Andrew M.
You're very welcome. Personally, it took me forever to get this type of problem straight in my head. Good luck.
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01/30/16
Erin S.
Andrew, I'm still not quite sure I understand could you explain in a little more detail?
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01/31/16
Andrew M.
You take the "part per hour" and multiply by the total time to achieve the whole job, or 100%.
For example: If Tom takes 3 hours to mow a 2 acre lawn then he does 1/3 of the lawn per hour. (1/3)(3) = 1 which designates the entire job being completed.
If Tom has help from a friend named Ben who could do the job in 2.5 hours ... that would be 2 1/2 hours alone for Ben or 5/2 hours. That means Ben does 1/(5/2) of the job per hour or 2/5 per hour of the whole job.
Together they do 1/3 + 2/5 of the job each hour.
If we need to figure out how long it takes them to mow the whole 2 acres working together then the sum of their hourly inputs multiplied by "x" hours set equal to 100% ... or 1 ... would be the equation:
x(1/3 + 2/5) = 1. Solve for x and you have the time it takes Tom and Ben to mow the lawn together...
x(5/15 + 6/15) = 1
x(11/15) = 1
x = 15/11
x = 1 4/11 hours.
Note when looking at your final answer it should be less than the smallest of either of the two men's time to do the job alone since even a little help would speed the process more than either doing the whole 2 acres alone. The final answer should be less than 2.5 hours which was Ben's time to do it alone. 1 4/11 hours is less than 2.5 hours so the answer makes sense.
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As a generic example of how to work this type of problem, I hope this helps.
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02/01/16
Pj J.
01/29/16