document.write( "Question 1163720: Ann, Beth, and Cathy start walking from the same place counter clockwise around a circular track with length 300 meters. Ann walks 120 meters/min, and Beth walks 100 meters/min, and Cathy walks 70 meters/min. In how many minutes will three of them meet again? \n" ); document.write( "

Algebra.Com's Answer #787895 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "The difference of rates  Ann-Beth  is 120-100 = 20 m/min.\r\n" );
document.write( "\r\n" );
document.write( "It means that  Ann and Bet will meet every 300/20 = 15 minutes somewhere on the circular track.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The difference of rates  Ann-Cathy  is 120-70 = 50 m/min.\r\n" );
document.write( "\r\n" );
document.write( "It means that  Ann and Cathy will meet every 300/50 = 6 minutes somewhere on the circular track.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now you take the Least Common Multiple of the integer numbers  15 and 6, which is 30.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is your ANSWER:  three of them will meet every 30 minutes.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The first meeting point is  at the distance 120*30 = 3600 m for Ann;  100*30 = 3000 m for Beth  and  70*30 = 2100 m for Cathy,\r\n" );
document.write( "\r\n" );
document.write( "but, although the distances along the circumference are different, they do represent the same point on the circular track, geometrically.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Notice that this meeting point is the same point they started from.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved and explained.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );