Math CentralQuandaries & Queries


Question from junna, a student:

a farmer would like to plant trees on one side of his lot which is 1/4 of a mile in a length His friend advised him that if he would plant the trees 5 feet farther apart,he would need 44 fewer trees.If the farmer would take the advice, how many trees would he plant?

Hi Junna,

There are 5280 feet in a mile so these are $\frac{5280}{4} = 1320$ feet in a quarter mile.

Suppose the farmer's initial plan is to plant the first tree and then plant the second tree $x$ feet away, and the third tree $x$ feet further on so there are $x$ feet between the trees. Thus, after the first tree the farmer needs $\frac{1320}{x}$ trees.

Suppose he increases the distance between the trees to $x + 5$ feet. How many trees will he need after the first tree? This is 44 less than the number in his initial plan. Solve for x.

Make sure you check your answer,

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