# The man with the hoe

The next riddle, very simple, is so stripped of mathematical difficulties that I hesitate to present it. However, like Edwin Markham's celebrated poem, I think it opens the way for interesting discussions.

It seems that, in exchange for five dollars, Hobbs and Nobbs agreed to plant a potato field for the farmer Snobbs. Nobbs can sow a row of potatoes in forty minutes and cover the groove with the same speed.

Hobbs, meanwhile, can sow a row in just twenty minutes, but in the time he covers two rows. Nobbs covers three.

Assuming that both men work constantly to sow the whole field, each of them sowing and covering their own, and also assuming that the field consists of twelve rows, as the illustration shows, How should the five dollars be divided so that each of the men received the amount proportional to the task accomplished?

#### Solution

If Nobbs can plant a row of potatoes in forty minutes, it would take 240 minutes to complete the six rows. As it covers them at the same speed, it would end with its part in 480 minutes, that is, in 8 hours.

Hobbs, working on the other six rows, would plant them in 120 minutes (one row every twenty minutes), and cover them in 360 minutes, making a total of 480 minutes, that is, 8 hours.

If Nobbs can plant a row of potatoes in forty minutes, it would take 240 minutes to complete the six rows. As it covers them at the same speed, it would end with its part in 480 minutes, that is, in 8 hours. Hobbs, working on the other six rows, would plant them in 120 minutes (one row every twenty minutes), and cover them in 360 minutes, making a total of 480 minutes, that is, 8 hours. Each of the men will do the same work in the eight hours that will take them to complete the planting of the whole field, so that to each of them will correspond \$ 2.50.