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?
Solution: 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)