Mowing Half a LawnDate: 03/31/2002 at 11:45:04 From: Jessica Pion Subject: Word Problem Chris and Lee are each responsible for mowing half of their 50-foot by 90-foot rectangular back yard. Chris starts mowing at an outside corner, gradually working toward the middle by mowing around the outside edges. If the mower cuts a 3-foot wide path, during which trip around the yard should Chris stop and Lee start mowing? I understand that the sides of the lawn get shorter every time Chris goes around. I don't understand what formula I would use to figure how much the lawn decreases. Thank you, Jessica Pion Date: 03/31/2002 at 18:37:08 From: Doctor Ian Subject: Re: Word Problem Hi Jessica, Let's draw a picture to help us visualize what's going on: 90 +----------------------------------+ | | | +----------------------------+ | | | | | | | +----------------------+ | | | | | | | | | | | | | | 50 | | | | | | | | +----------------------+ | | | | | | | +----------------------------+ | | | +----------------------------------+ Each of the strips is 3 feet wide, so after n trips around the yard, thesituation looks like this: 90 +----------------------------------+ | | | +----------------------------+ | | | | | | | +----------------------+ | | | | | 90 - 6n | | | | | | 50 - 6n | | | 50 | | | | | | | | +----------------------+ | | | | | | | +----------------------------+ | | | +----------------------------------+ So after some number of trips, the amount of yard left for Lois to cut, (90 - 6n)(50 - 6n) is going to be less than half of the total amount of yard, (1/2)(90)(50) which means that you want to find n such that (90 - 6n)(50 - 6n) < (1/2)(90)(50) Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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