Be a good mathematician
Johnny and Sam need 84 hours to complete a math project together, each working at a constant rate. If Johnny works on it alone, he needs 500 hours to complete it.
How many hours does Sam need to complete 26 identical math projects alone?
Assume the boys have a constant rate.
The answer is 2625.
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1 solution
Relevant wiki: Related Rates - Word Problems - Intermediate
Let Johnny be J and Sam be S.
J+S=84 hours [rate is 8 4 1 of the project per hour]
J=500 [rate is 5 0 0 1 of the project per hour]
So, S = 8 4 1 - 5 0 0 1 = 2 6 2 5 2 6 of the project completed per hour
We multiply 2 6 2 5 2 6 by 2625 (the denominator) because we wanted 26 projects and 26 is there already.
So Sam takes 2625 hours to complete 26 projects.