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How long will it take to mow the runway

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It's been a while since I posted a puzzler, so here's one for you (and this is a real scenario).  A friend recently purchased a second hand lawn mower.  It has a 48inch cutting area.  They purchased the lawn mower to mow their lawn but also to mow their planned grass strip airfield.  

The runway is 1800 feet long and 60 feet wide.  The runway is 7-25 (which means it's 70 degrees in one direction and 250 in the other).  As mentioned earlier the mower has a 48 inch blade, and he'll overlap the cutting by approx. 12 inches on each pass.  The mower cuts at 8 mph.  So the question is, how long will take my friend to mow his grass strip?

Comments

Gravatar Image1 - I guess just under 1 hour.

For each pass the lawnmower will cut 3 feet (48 inches - 12 inch overlap). So 60 feet divided by 3 feet will mean that 20 passes will be needed to be made and 20 times 1800 feet will mean 36,000 feet will be covered in those 20 passes. So if you take this number and divide by the number of feet in a mile (5,280) you will find that the total # of miles covered in 20 passes is 6.82 miles and therefore since the mower cuts at 8 mph your friend should be done in less than 1 hour. Again, this assumes that my math is correct. :)

Gravatar Image2 - Forever.

It'll be like the Forth Road Bridge. Once you've finished at one end it'll be time to start at the other end again.

I would attempt to work it out, but there is just one problem. { Link }

Gravatar Image3 - I get it to 53 minutes, assuming I got all the weird US measurements right. Emoticon

The runway is 60 ft wide = 720 inches.
The first pass is 48 inches wide, the following are 36 inches (12 inch overlap). 720-48 leaves 672 inches to cut in 36 inch passes, which is 18.6 passes. This makes a total of 19.6 passes, which really mean 20 passes.

20 passes at 1800 ft = 36000 ft, which is 6.82 miles. With a speed of 8 miles per hour, it will take 0.8525 hours, or 52.95 min.

Gravatar Image4 - I'm thinking there is some speed reduction at the end of each pass as the mower slows, stops, reverses direction, and accelerates again. Anyone got some empirical data for the deceleration / acceleration of a mower ? Once I figure that it, I should have a better guess-timate.

Gravatar Image5 - What about taking into account the added friction going against the nap of the grass? Or how about wind resistance? They will definitely impact mowing time.

Oh-oh, don't forget the moisture content of the grass. That could really bog things down.

Is the mower gas or diesel? Hmmm.

Gravatar Image6 - I would estimate about 1hr 45mins due to fuel and drink stops!

Gravatar Image7 - the word on the street is this grass runway is south of the Mason-Dixon line so the drink *stops* may not apply. These mowers have drink holders !

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