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A contractor contracts to finish a piece of work in 30 days,
and immediately employs 15 men upon it;
at the end of 24 days the work is only half done.
How many additional men must he employ to fulfill the contract?


Suggested Solution (Shawn Ingraham, WWU student)
Assume contract is to build 100 things. After 24 days, only 50 are complete, implying an average of 2.08 buildings/day. We can assume each of the 15 men contribute an equal share of the 2.08 buildings/day, or each contributes 2.08/15 = 0.1388 buildings per day per man. To complete the contract, 50 buildings need to be completed in 6 days, or an average needed of 50/6 = 8.33 buildings/day. Since each man can build 0.1388 buildings/day, we solve the equation 8.33 = 0.1388x, where x is the total number of men needed for ther necessary pace. Now, x=60 men, but since 15 men are already hired, contarctor needs to hire an additional 45 men.

Suggested Solution (Tommy Lingbloom, WWU student)
Let t1=time passed, t2=time remaining, w1=work completed, w2=work remaining, m1=men used, and m2=men needed. Then we have the combined equation: t1* w1*m1 = t2*w2*m2. [Check units?]. But this means that (24)(1/2)(15)=(6)(1/2)(m2, or that m2=60 men, which is 45 men more than the initial 15 men.

Source: Charles Pendlebury's Arithmetic (London: G. Bell & Son, 1918)