How Much Material to Purchase?
Date: 11/01/97 at 16:58:05 From: kim peterson Subject: Ramp Sanchez warehouse wants to install a 3-foot wide ramp from the level floor to the top of the 4-foot high platform. A regulation states that for every 2 feet that such a ramp rises vertically, the bottom of the ramp must be placed 5 feet farther from the bottom of the platform. If the material for the top surface of the ramp comes in 3-foot widths and whole-foot lengths, what is the minimum length of the material that must be purchased?
Date: 11/03/97 at 10:23:10 From: Doctor Pipe Subject: Re: Ramp Kim, A good way to understand this problem and its solution is to draw a picture. Draw the picture so that each half inch that you draw represents one foot in the problem - the line representing the four feet from the floor to the platform will be two inches long). Start by drawing a horizontal line to represent the floor. Then draw a vertical line up from the floor to represent the four feet from the floor to the platform. Finally, draw another horizontal line from the top of the vertical line to represent the platform. Label the floor, the platform, and the four feet from the floor to the platform. Now, the regulation says that for each two feet that a ramp rises vertically, the bottom of the ramp must be placed 5 feet from the bottom of the platform. Since our ramp needs to rise four feet, the bottom of the ramp needs to be 10 feet from the bottom of the platform. Measure and mark the spot on your drawing that is on the floor ten feet from the bottom of the platform (remember that each half inch in your drawing represents a foot in the problem). Now draw a straight line from the edge of the platform to the point on the floor. This line represents a ramp built to comply with the regulation. Notice that you have drawn a right triangle. To calculate the length of the ramp, apply the Pythagorean theorem. The ramp is the hypotenuse, the length of the floor under the ramp (10 feet) is the length of one leg, and the height of the platform (4 feet) is the other leg. When writing down your final answer, remember that the material for the top of the ramp is sold only in whole-foot lengths. This means that you can't buy 10.77 feet. If you need 10.77 feet of material then you have to buy twelve feet. You'll also want to sweep the ramp each hour so no one slips on it! -Doctor Pipe, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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