document.write( "Question 823513: A car has wheels which are 140 cm in diameter. How many complete revolutions per minute does each wheel make when the car is running at a speed of 66 km/hr? \n" ); document.write( "
Algebra.Com's Answer #495576 by math-vortex(648) $\"\"$ $\"About$
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "A car has wheels which are 140 cm in diameter. How many complete revolutions per minute \r\n" );
document.write( "does each wheel make when the car is running at a speed of 66 km/hr?\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "This is a unit conversion problem. We will work our way through a series of conversions to get \r\n" );
document.write( "to the desired information. We will need to keep close eye on the units of our answers as we \r\n" );
document.write( "proceed.\r\n" );
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document.write( "We are asked to find the number of complete revolutions per minute. In other words, how \r\n" );
document.write( "many times will the wheel make a complete turn in a one-minute period. Let's start with what \r\n" );
document.write( "we know:\r\n" );
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document.write( "The wheels have a diameter of 140 cm. In order to find the length of one revolution of the \r\n" );
document.write( "wheel, we need to know the circumference C of the wheel. The formula for the circumference \r\n" );
document.write( "of a circle is \"the diameter times [pi].\" Estimate [pi] as 3.14.\r\n" );
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document.write( "C = [140 cm] * [3.1416] = 439.82 cm\r\n" );
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document.write( "So, each time the wheels make one revolution the car travels 439.82 cm. We can write this as \r\n" );
document.write( "439.82 cm per revolution, or 439.82 cm/rev.\r\n" );
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document.write( "We know that the car is traveling as 66 km per hour. Remember we want to know the number \r\n" );
document.write( "of revolutions in one minute. Let's translate 66 km/hr in km per minute. \r\n" );
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document.write( "Since the car is traveling at 66 km per hour that means it travels 66 km in one hour. There are \r\n" );
document.write( "60 minutes in one hour, so the car travels 66 km in 60 minutes. We want to know how far the \r\n" );
document.write( "car travels in one of those minutes, so we divide:\r\n" );
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document.write( "[66 km/hr] / [60 min/hr] = 1.1 km/min\r\n" );
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document.write( "The car travels 1.1 km per minute.\r\n" );
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document.write( "Notice that our car speed is expressed in km, but or wheel revolutions are expressed in cm. \r\n" );
document.write( "We need to translate one of those rate. Let's rewrite the car speed in cm/min. We will do this \r\n" );
document.write( "in two steps for the sake of clarity. There are 1000 meters (m) in one km. We want to know \r\n" );
document.write( "how many meters there are in 1.1 km, so we multiply:\r\n" );
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document.write( "[1.1 km/min] * [1000 m/km] = 1100 m/min.\r\n" );
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document.write( "We repeat this process to convert meters to cm. There are 100 cm in one meter. We want to \r\n" );
document.write( "know how many centimeters there are in 1100 m, so we multiply, \r\n" );
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document.write( "[1100 m/min] * [100 cm/min] = [110000 cm/min]\r\n" );
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document.write( "Now we know that a car traveling at a constant speed of 66 km per hour, travels 110000 cm \r\n" );
document.write( "each minute. We also know that the car travels 439.82 cm for each revolution of the wheel. \r\n" );
document.write( "We would like to know how many of those revolutions will fit in 110000 cm, so we divide\r\n" );
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document.write( "[110000 cm/min] / [439.82 cm/rev] = [250.10 rev/min]\r\n" );
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document.write( "The wheels make 250.10 revolutions each minute. That's 250 complete revolutions, plus a \r\n" );
document.write( "little bit more.\r\n" );
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document.write( "As you get better at these unit conversion problems, it's common to see the problem laid out \r\n" );
document.write( "in a long string of conversions, sometimes called dimensional analysis. Here's what that looks \r\n" );
document.write( "like for your problem:\r\n" );
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document.write( "[66 km/hr] / [60 min/hr] * [1000 m/km] * [100 cm/m] / [439.82 cm/rev  = [250.10 rev/min]\r\n" );
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document.write( "Hope this helps! Feel free to email me with a follow-up question if you have questions about \r\n" );
document.write( "the explanation.\r\n" );
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document.write( "Mrs. Figgy\r\n" );
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