AMC12B2003: Moe uses a mower to cut his 90-by-150-ft lawn

[brightmind]

Moe uses a mower to cut his rectangular 90 foot by 150 foot lawn. The swath he cuts is 28 inches wide, but he overlaps each cut by 4 inches to make sure that no grass is missed. He walks at a rate of 5000 feet per hour while pushing the mower. Which of the following is closest to the number of hours it will take Moe to mow his lawn? 0.75 0.8 1.35 1.5 3

I assume that he walks along the 90 ft side. Because the swath is 28/12 ft wide, he will have to walk 150/(28/12)=450/7 times along the 90 ft side. And because he overlaps each cut by 4/12 ft, he actually walks 90/(4/12)×2×4/12=180 ft each time along the 90 ft side. So the total dictance he has to walk is about 450/7×180=81000/7ft.His speed is 5000 ft/hr, so he has to walks for about 81000/7: 5000=2.3 hr?????

 

[soroban]

Hello, brightmind!

Moe uses a mower to cut his rectangular 90 foot by 150 foot lawn. The swath he cuts is
28 inches wide, but he overlaps each cut by 4 inches to make sure that no grass is missed.
He walks at a rate of 5000 feet per hour while pushing the mower.
Which of the following is closest to the number of hours it will take Moe to mow his lawn?

. . . \(\displaystyle (a)\;0.75 \qquad (b)\;0.8 \qquad (c)\;1.35 \qquad (d)\;1.5 \qquad (e)\;3\)

His swath is actually 24 inches wide (two feet).
Going down the length of the lawn, we makes 45 passes across the lawn.
At 150 feet per pass, he travels: \(\displaystyle 150 \times 45\:=\:6750\) feet.

\(\displaystyle \text{At a speed of 5000 ft/hr, this will take him: }\:\frac{6750}{5000} \:=\:1.35\text{ hours . . . answer (c)}\)

 

[brightmind]

What about the fact that he overlaps 4 inches each cut, does it tell us that the total time must be longer than if he does not overlap each cut?????????

 

[Denis]

To start, your 2.3 hours for no overlap is not correct; should be ~1.2
Soroban's 1.35 hours is correct, and is more than if there was no overlap.