9. Two Diggers. This curious problem is actually more difficult than it might seem at first glance. Abraham, a frail old man, contracted to dig a ditch for 2 dollars. He hired Benjamin, a strapping young man, to help him. The money was to be divided in proportion to each man's digging abilities. Abraham digs as fast as Benjamin shovels out the dirt, and Benjamin digs four times as fast as Abraham shovels out the dirt.

How should they divide the money? Of course, we assume that the strength ratio of the old man to the young man is the same for digging as it is for shoveling.
9. Abraham \((A)\) should receive one third of the total sum, while Benjamin (B) should receive two thirds. For instance, let \(B\) be able to dig a ditch in 2 hours and throw out all the soil in 4 hours. Then \(A\) can dig a ditch in 4 hours and throw out all the soil in 8 hours. Therefore, when digging the ditch, their strengths are in the ratio of 2 to 4, and when throwing out the soil, in the ratio of 4 to 8 (i.e., the ratio of their strengths remains unchanged). In this case, \(A\) can dig a ditch in the same time it takes \(\bar{L}\) to throw out all the soil (4 hours), and \(B\) can dig a ditch in one quarter of the time \(A\) spends on throwing out the soil. Any other specific numbers that satisfy the conditions of the problem will lead to two similar ratios of the strengths of both diggers. Therefore, Abraham should receive one third of the total sum, and Benjamin should receive twice as much, i.e., two thirds.