document.write( "Question 1204230: Bill's bike wheels have a 26-in. diameter. The odometer on his bike counts the number of times a wheel rotates during a trip. If the odometer counts 200 rotations during the trip from Bill's house to school, how many feet does Bill travel? Round to the nearest foot. \n" ); document.write( "
Algebra.Com's Answer #840350 by math_tutor2020(3817)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "Answer: 1361 feet\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Explanation\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "d = diameter = 26 inches \n" ); document.write( "C = circumference = perimeter around the circle\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "C = pi*d \n" ); document.write( "C = 3.14*26 \n" ); document.write( "C = 81.64 \n" ); document.write( "This is the approximate distance around the wheel. It's approximate because pi = 3.14 is approximate. \n" ); document.write( "Use more decimal digits of pi to get a better approximation.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "1 full rotation of the wheel will move the bike forward roughly 81.64 inches. \n" ); document.write( "This assumes that there isn't any slipping. Slipping is when the wheel spins some amount different compared to how the bike moves. Example: the wheel rotates 5 feet but the bike only would move forward 2 feet.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "200 such rotations would move the bike forward 200*81.64 = 16,328 inches.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Divide by 12 to go from inches to feet \n" ); document.write( "16328/12 = 1,360.66666666667 approximately\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "When rounding to the nearest foot we get 1361 feet as the final answer.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "As a shortcut, we can type this into the calculator \n" ); document.write( "pi*26*200/12 \n" ); document.write( "where we let the calculator handle the decimal digits of pi for the best accuracy possible. \n" ); document.write( "The result of which is approximately 1,361.35681655558 which rounds to 1361 feet \n" ); document.write( "Either way we'll get the same answer.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Side note: 1361 ft = 1361/5280 = 0.2578 miles approximately \n" ); document.write( " \n" ); document.write( " |