How far must a riding mower travel?

Question

section of the yard is 68 feet wide and 104 feet to the street. Cut perpendicular to the street. Cutting width of mower is 36 inches. The mower overlaps exactly 6 inches per pass.

Answer 1

HI JH!

 

Let's break this down into what the mower is doing.  First, we know the mower cuts a strip 3 feet wide (=36 inches).  Since it overlaps 6 inches on any pass where it is cutting next to another strip it cut, it is cutting a new strip that is 6 inches narrower than the mower's full width.  Thus, on any pass where it is cutting next to where it already cut, it is cutting a strip 3 ft - 6 in = 3 ft - 0.5 ft = 2.5 ft wide.

 

I will assume that the mower either cannot or does not want to cut beyond the bounds of this rectangle.  Therefore, on the first pass, it will cut a full 3-foot-wide strip.  If it cuts in the orientation you describe, that means it is cutting ALONG the 104 ft dimension of the yard, and the strips stack up ACROSS the 68-foot dimension of the yard.  So, after the mower cuts the first 3-foot-wide strip, the remaining unmowed width of the yard is 68 - 3 = 65 ft.

 

For the rest of the time, the mower will then cut 2.5-foot-wide strips, because it is always cutting next to where it has already cut.  The question is, then, how many 2.5-foot-wide strips go into 65 feet (and does it divide evenly)?

 

So we calculate:  65/(2.5) = 26  (so it does divide evenly).

 

This means that the mower need to cut 26 more rows to mow the rest of the yard.  And it had already mowed the first 3-foot-wide strip at that point.  So that means it makes a total of 27 passes along the 104-foot dimension of the rectangle.

 

From this information, can you calculate the total distance the mower travels?  I hope this sets you in the right direction, but if you have any more questions, just let me know!

Answer 2

The way I understand the problem is that the mower is going up and down the 104 ft over and over until it covers the 68 ft. So the question is how many times does it go back and forth. 

 

The first time it covers 3 ft wide and then each other time it covers an additional 2.5 feet (36-6 inches). 

 

So after the 1st cut, we have 68-3 or 65 more ft to cut. So take 65/2.5 or 26 more times to finish the job. So in total the mower had 27 times traveling the 104 ft each time. Therefore it traveled 104(27) or 2808 ft in total.