Maxine and Sammie have the same size lawn. Maxine can mow the lawn in 24 minutes and Sammie can mow the lawn in 36 minutes. At what time will Sammie have twice as much lawn to mow as Maxine?

Maxine and Sammie have to also mow their parking strips that are the same size. Maxine can mow the parking strip in 6 minutes and Sammie can mow the parking strip in 9 minutes. At what time will Sammie have twice as much grass to mow as Maxine?

Answer: A) 18.2 minutes

B) 4.5 minutes.

Step-by-step explanation:

A) Maxine can mow one lawn in 24 minutes, so the rate of work is:

1/24 of the lawn per minute.

Sammie can mow one lanw in 36 minutes, so the rate of work is:

1/36 of the lawn per minute.

The amount of the lawn that each has left to lawn by the minute x is:

Maxine = 1 - (1/24) * x

Sammie = 1 - (1/36) * x

we want to find the value of x such that:

2 * (1 - (1/24) * x) = 1 - * (1/36) * x

which means that the amount that Sammie has left is two times the amount that Maxine has left to mow.

2 - (1/12) * x = 1 - (1/36) * x

2 - 1 = (1/12 - 1/36) * x

1/0.055 = x = 18.2

by the minute 18.2

B) Similar to before, here the rates are:

For Maxine, R = 1/6

For Sammie, R = 1/9

The amount they have left to mow by minute x is:

Maxine = 1 - (1/6) * x

Sammie = 1 - (1/9) * x

We want to solve, similar to before.

2 (1 - (1/6) * x) = 1 - (1/9) * x

2 - (1/3) * x = 1 - (1/9) * x

2 - 1 = (1/3 - 1/9) * x

1 = (2/9) * x

1*9/2 = x = 4.5

So here the solution is 4.5 minutes.