Cleaning the IceDate: 09/09/97 at 22:31:11 From: Lauren Jones Subject: Area Dear Dr. Math, Here is my question: Venski is fascinated by the ice cleaning machine as it scrapes the ice between periods of a hockey game. The hockey rink is a rectangle, 120 ft. by 60 ft. The scraper cleans a 4 ft wide strip. If the machine starts at one corner and moves around and around the rink toward the center, on which trip around will it have half the area of the rink clean? I have drawn a picture and divided and multiplied. I am having trouble comprehending all of the numbers. Respectfully yours, Lauren Jones Date: 09/10/97 at 16:48:30 From: Doctor Barney Subject: Re: Area I cannot think of any shortcut to solve this problem, so let's just figure out what half the area of the rink is and then add up how much area the "Zamboni" cleans on each trip around the rink. A = 120 x 60 = 7,200 square feet, so half of that area is 3,600 sq.ft. first time around = 4 x (120+56+116+52) = 1,376 second time around = 4 x (112+48+108+44) = 1,248 total cleaned so far 2,624 third time around = 4 x (104+40+100+36) = 1,120 total cleaned so far 3,744 So, near the end of the third trip around the rink half of the area will have been cleaned. Notice that each time the machine turns a corner you need to subtract four feet from the next side because it has already cleaned the first four feet of that side where it turns the corner. For more fun try this one: How many trips around will the machine have made by the time all of the area is cleaned? -Doctor Barney, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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