document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=257443>Question 257443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Josh’s bicycle has 28-inch-diameter wheels and Julian’s has 14-inch-diameter wheels. Josh’s wheel rotates twice for every three rotations of the pedals; Julian’s wheel rotates three times for every two rotations of the pedals. Josh rotates the pedals twice as quickly as Julian (twice as many rotations per unit of time). Julian takes 8 minutes to bicycle one mile. How much time will Josh take? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #189442 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=189442\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Josh’s bicycle has 28-inch-diameter wheels and Julian’s has 14-inch-diameter wheels. Josh’s wheel rotates twice for every three rotations of the pedals; Julian’s wheel rotates three times for every two rotations of the pedals. Josh rotates the pedals twice as quickly as Julian (twice as many rotations per unit of time). Julian takes 8 minutes to bicycle one mile. How much time will Josh take?\r<BR>\n" );
document.write( "\n" );
document.write( "(60 minutes in an hour) X (N revolutions per minute) X ((D wheel diameter in inches) X pi  per revolution) DIVIDED BY (5280 feet in a mile) times (12 inches in a foot) =<BR>\n" );
document.write( "(speed in miles per hour)<BR>\n" );
document.write( "60*(min/hr)*N*(rev/min)*(D*pi)*(in/rev) DIVIDED BY 5280*(ft/mi)* 12 * in/ft<BR>\n" );
document.write( "60*N*D*pi*(in/hr) DIVIDED BY 5280*12*(in/mile)<BR>\n" );
document.write( "(60*N*D*pi)/(5280*12) miles/hr<BR>\n" );
document.write( "(5*N*D*pi)/5280 miles/hr  (60/12=5)<BR>\n" );
document.write( "(N*D*pi)/1056 miles/hr    (1056*5=5280)\r<BR>\n" );
document.write( "\n" );
document.write( "1 mile / 8 min * 60 minutes / 1 hr<BR>\n" );
document.write( "1/8 * (miles/min) * 60 * (min/hr)<BR>\n" );
document.write( "1/8 * 60 miles/hr<BR>\n" );
document.write( "7.5 miles/hr or 1/8 mile/min\r<BR>\n" );
document.write( "\n" );
document.write( "for Julian 7.5=(N*D*pi)/1056<BR>\n" );
document.write( "          7920=N*D*pi<BR>\n" );
document.write( "          7920=N*14*pi<BR>\n" );
document.write( "          180.0724498983=N in rev/min<BR>\n" );
document.write( "          1440.5795991861 revolutions in 8 minutes <BR>\n" );
document.write( "         10804.3469938955 rev/hr  (60 min/hr)\r<BR>\n" );
document.write( "\n" );
document.write( "Josh’s wheel rotates twice for every three rotations of the pedals; Julian's wheel rotates three times for every two rotations of the pedals. Josh rotates the pedals twice as quickly as Julian\r<BR>\n" );
document.write( "\n" );
document.write( "2 rev / 3 pedal   or 2/3 rev per pedal  or 2/3*28*pi inches per pedal<BR>\n" );
document.write( "                            58.643062867 inches per pedal<BR>\n" );
document.write( "3 rev / 2 pedal   or 3/2 rev per pedal  or 3/2*14*pi inches per pedal<BR>\n" );
document.write( "                          65.9734457254 inches per pedal<BR>\n" );
document.write( "and Josh pedals twice as fast so Josh covers 117.286125734 inches in same time it takes Julian to go 65.9734457254 inches<BR>\n" );
document.write( "a ratio of 1.7777777778 to 1\r<BR>\n" );
document.write( "\n" );
document.write( "8 minutes / 1.7777777778 = 4.4999999999 = 4.5\r<BR>\n" );
document.write( "\n" );
document.write( "Josh will take 4.5 minutes\r<BR>\n" );
document.write( "\n" );
document.write( "                        \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );