document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110910>Question 1110910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Your car's speedometer is geared to accurately give your speed using a certain tire size: 15\" diameter wheels (the metal part) and 4.3\" tires (the rubber part).\r<BR>\n" );
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document.write( "(a) If your car's instruments are properly calibrated, how many times should your tire rotate per second if you are travelling at 55 mi/hr? <BR>\n" );
document.write( "rotations = <BR>\n" );
document.write( " Report answer accurate to 3 decimal places.\r<BR>\n" );
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document.write( "(b) You buy new 5.4\" tires and drive at a constant speed of 65 mph (according to your car's instrument). However, a cop stops you and claims that you were speeding. How fast did the radar gun clock you moving? <BR>\n" );
document.write( "actual speed = ?mph <BR>\n" );
document.write( "Report answer accurate to the nearest whole number.\r<BR>\n" );
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document.write( "(c) Then you replace your tires with 3.45\" tires. When your speedometer reads 30 mph, how fast are you really moving? <BR>\n" );
document.write( "actual speed = ?mph <BR>\n" );
document.write( "Report answer accurate to 1 decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #725962 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=725962\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I didn't check all of tutor theo's analysis, but his process seems right and so his answers should be good.<br><BR>\n" );
document.write( "It is easy to show that his answers for parts b and c are right.<br><BR>\n" );
document.write( "A speedometer determines the car's speed by counting the revolutions of the axle.  It shows the correct speed if the tires being used are the ones for which the speedometer was calibrated.<br><BR>\n" );
document.write( "If you put on larger tires, the circumference of the tire is larger, so you go farther on each revolution, so your speed is higher than what the speedometer shows; if you put on smaller tires, you speed is lower than what the speedometer shows.<br><BR>\n" );
document.write( "Since the ratio of the circumferences of two different size tires is the same as the ratio of the diameters, the ratio of actual speed to the speed shown by the speedometer is just the ratio of the diameters.<br><BR>\n" );
document.write( "For part b of the question then...<BR>\n" );
document.write( "The diameter of the wheel for which the speedometer is calibrated is 15+2*4.3 = 23.6 inches.  When you put on 5.4 inch tires, the diameter is 15+2*5.4 = 25.8 inches.<br><BR>\n" );
document.write( "If the speedometer shows 65 mph when you are using the larger tires, your actual speed is 65 * (25.8/23.6) = 71.06 mph.<br><BR>\n" );
document.write( "For part c, the new diameter of the wheel is 15+2*3.45 = 21.9 inches.  So when the speedometer reads 30 mph with the smaller tires, your actual speed is 30 *(21.9/23.6) = 27.84 mph. </SPAN>\n" );
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