6th grade summer homework question! please help!?

Question

Maxine & Sammy have the same amount of lawn.

maxine can mow the lawn in 24 min.
sammy can mow the lawn in 36 min.

At what time will sammy have twice as much lawn to mow as maxine?

Answer 1

In 1 min Maxine can mow = 1/24 parts of the lawn.
In 1 min Sammy can mow = 1/36 parts of the lawn.

Suppose after 't' minutes, Sammy will have twice as much lawn to mow as Maxine.
In 't' mins. Maxine can mow = t/24 parts of the lawn.
In 't' mins. Sammy can mow = t/36 parts of the lawn.

After 't' mins. the amount of lawn to be mowed:
Maxine's lawn = 1 - t/24
Sammy's lawn = 1 - t/36

By problem, 2(1 - t/36) = (1 - t/24)
2 - t/18 = 1 - t/24
t/18 - t/24 = 1
t = 72

Ans: 72 minutes

Answer 2

I assume you meant to ask at what time will Sammy have twice as much lawn LEFT to mow as Maxine.

The amount of lawn left to mow after x minutes:

for Maxine = 1 - x/24
for Sammy = 1 - x/36

When Sammy has twice as much lawn LEFT to mow we have:

2(1 - x/24) = 1 - x/36
2 - x/12 = 1 - x/36
1 = x/12 - x/36 = 3x/36 - x/36 = 2x/36 = x/18
18 = x

The answer is 18 minutes.

Answer 3

Let M and S represent their working speeds, respectively.
M = 1/24
S = 1/36
1-Mt = 2(1-St), t ≤ 24 min.
1-t/24 = 2(1-t/36)
Multiply by 72,
72-3t = 144 - 4t
t = 72 min > 24 min.

Since Maxine can finish in 24 min, the case described in the problem can never happen.
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Ideas: Pay attention to the time restriction: t ≤ 24 min. Otherwise, your answer doesn't make sense.

Answer 4

72 min

Answer 5

YAY! i can answer this. im in 8th. wait a minute...u cant get the answers from other ppl. tsk tsk man tsk tsk. *i used to do the same thing* WOO would you look at the time.

Answer 6

72 min.