Dimishing returns word problem help

Question

Mr. K mows the lawn in 24 minutes. Mr.Z mows in 36 minutes. The question is after how many minutes will Mr.Z have twice as much lawn to mow as Mr.K. How do you solve this problem with equation algebraically?

Answer 1

Try this (I'll put asterisks every time I give a little more of a hint):

You're probably trying to write equations for how fast they mow--at least, that was my first thought, but try writing equations for how much lawn they have left to mow.

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Assuming it's the same size lawn, let's give the lawn a value of 1, since it's 1 whole lawn (if the question were given in percents, we'd make it 100).

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How much lawn do they each have left after 1 minute? After 2 minutes? After m minutes?

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You're going to have three equations and three variables. Make your first equation to find how much lawn K has left after m minutes, and your second to find out how much lawn Z has after m minutes. Can you figure out your third equation?

(equations follow, so if you want to work it out for yourself based on the above, stop now

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After 1 minute, K has mowed 1/24 of the lawn, so he has 23/24 left. After 2 minutes, he has 22/24 left. So after m minutes, he has 1-m/24 left. Follow similar reasoning with Z to get the first two equations:

k=1-m/24

z=1-m/36

That's two equations and three variables, but we actually want to solve it. Specifically, we want to know when z=2k. So that's our third equation.

A little substitution and solve for m...