In November 1905, the Bangor Daily News published the following problem:
A gentleman wishes to dig a trench, 100 feet in length, paying for the work $100 – or an average of $1 a foot. He employs two laborers, agreeing to give the first laborer the sum of 75 cents per foot and the second $1.25 per foot. Now, how many feet – that is, what percent of the trench – must each laborer dig to earn $50?”. The poser was signed “Mystified”.
A journalist named Annie Lawless republished this problem on the 2 December 1977 issue of Bangor Daily News. She wondered if this problem, which mystified many of the so-called experts in 1905, could perhaps be easily solved using the “new math” that was taught in schools during the 70’s.
However, Mrs. Lawless apparently failed to realize that one respondent back in 1905 saw through the fallacy of this problem, which he wrote:
Perhaps, “Mystified” can answer this. If a cow costing $95 gives 20 quarts of milk a day, how high can a grasshopper jump without getting out of breath?
You should have realized by now that this problem is flawed and unsolvable. If you are curious why no solution exists, here’s the simplest explanation that I could come up with.
The problem stated that a man wishes to dig a trench, 100 feet in length, paying for the work $100. This means that each foot costs $1 labor. Now, the problem also stated that the man is wiling to pay $1.25 per foot to one of the workers. To calculate how many feet this worker have to dig to earn $50, just divide $50 by $1.25 per foot, which gives us the answer of 40 feet. Therefore, the worker with a wage of $1.25 per foot needs to dig 40 feet before he could earn $50.
This means that the other worker with a wage of 75 cents or $0.75 per foot would have to dig the remaining 60 feet. To determine the total wage of this working, just multiply $0.75 by 60:
$0.75 × 60 = $45
Thus, when one of the workers earns $50, the other worker won’t be able to earn $50 as well because there’s not enough work remaining for the other worker to earn that much.