SOLUTION: I own a 2006 Honda CRV. Last spring, I was still driving on the original tires. I looked at them and decided that I had worn down enough tread, so it was time to buy a whole new se

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: I own a 2006 Honda CRV. Last spring, I was still driving on the original tires. I looked at them and decided that I had worn down enough tread, so it was time to buy a whole new se      Log On

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Question 371997: I own a 2006 Honda CRV. Last spring, I was still driving on the original tires. I looked at them and decided that I had worn down enough tread, so it was time to buy a whole new set of tires. Let us say that I began with 16-inch tires (11/16 inch of tire tread depth). If I drove at 60mph, how many revolutions per hour would one new tire make? Let us say that I drove 40,000 miles on those tires so that the tread depth wore down to 3/16 inch. If I drove at 60mph, how many revolutions per hour would one worn tire make? Calculate the difference in revolutions per hour between the new tire and the worn tire.
Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
"I own a 2006 Honda CRV. Last spring, I was still driving on the original tires. I looked at them and decided that I had worn down enough tread, so it was time to buy a whole new set of tires. Let us say that I began with 16-inch tires (11/16 inch of tire tread depth). If I drove at 60mph, how many revolutions per hour would one new tire make? Let us say that I drove 40,000 miles on those tires so that the tread depth wore down to 3/16 inch. If I drove at 60mph, how many revolutions per hour would one worn tire make? Calculate the difference in revolutions per hour between the new tire and the worn tire."

circumference = diameter * pi
circumference new tire = 16 inches * pi = 16pi inches
11/16 inch tire tread depth - 3/16 inch tire tread depth = 8/16 inch tire tread depth
8/16 inch = 1/2 inch --> diameter old tire = 15.5 inches
circumference old tire = 15.5pi inches
60 mph = 60 miles in 1 hour
new = 60 miles * 5280 ft/mile * 12 inches/ft * 1/16pi rev/inches
new = 3801600/16pi revolutions
new = 75630.428957 rounded to 6 places revolutions in 60 miles
old = 60 * 5280 * 12 * 1/15.5pi revolutions
old = 3801600/15.5pi revolutions
old = 78070.120214 rounded to 6 places revolutions in 60 miles
new - old = 75630.428957 - 78070.120214 = -2439.691257 revolutions
75630 - 78070 = -2440 revolutions
old tires make 2440 revolutions more in 60 miles at 60 mph

if i made a mistake, someone let me know, and i apologize if i did