document.write( "Question 271644: Cyclist A started his journey on cycle at 7:30 a.m. at a speed of 8 km/h. After 30 minutes, cyclist B started from the same place but with a speed of 10 km/h. At what time did B overtake A? \n" ); document.write( "
Algebra.Com's Answer #198824 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Cyclist A started his journey on cycle at 7:30 a.m. at a speed of 8 km/h. After 30 minutes, cyclist B started from the same place but with a speed of 10 km/h. At what time did B overtake A?
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "(The other tutor added 2 hours to 7:30am and got 9:30am. He should\r\n" );
document.write( "have added it to 8:00am to get 10:00am.)\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "First let's do it in our heads without algebra, \r\n" );
document.write( "then we'll do it with algebra:\r\n" );
document.write( "\r\n" );
document.write( "In our heads:\r\n" );
document.write( "\r\n" );
document.write( "When B starts at 8am, A has been going 8 km/h for half an hour, so A\r\n" );
document.write( "has a 4 km head start on B.  B then chases A going 2 km/h faster \r\n" );
document.write( "than A, so B is approaching A at 2 km/h.  At that catch-up rate it will \r\n" );
document.write( "take B 2 hours to make up A's 4 km head start.  So B will overtake A \r\n" );
document.write( "at 10am.\r\n" );
document.write( "\r\n" );
document.write( "By algebra.\r\n" );
document.write( "\r\n" );
document.write( "Let t be the time it takes B to overtake A\r\n" );
document.write( "\r\n" );
document.write( "Make this chart\r\n" );
document.write( "\r\n" );
document.write( "     Distance     Rate    Time \r\n" );
document.write( "A\r\n" );
document.write( "B\r\n" );
document.write( "\r\n" );
document.write( "Fill in t for B's time\r\n" );
document.write( "\r\n" );
document.write( "     Distance     Rate    Time \r\n" );
document.write( "A\r\n" );
document.write( "B                          t\r\n" );
document.write( "\r\n" );
document.write( "A's time is a half hour longer than B's time\r\n" );
document.write( "since he started half an hour sooner, so fill in\r\n" );
document.write( "t+.5 for A's time:\r\n" );
document.write( "\r\n" );
document.write( "     Distance     Rate    Time \r\n" );
document.write( "A                         t+.5\r\n" );
document.write( "B                          t\r\n" );
document.write( "\r\n" );
document.write( "Their rates are given so fill those in:\r\n" );
document.write( "\r\n" );
document.write( "     Distance     Rate    Time \r\n" );
document.write( "A                  8      t+.5\r\n" );
document.write( "B                 10       t\r\n" );
document.write( "\r\n" );
document.write( "Now use \"DISTANCE=RATE%2ATIME\" to\r\n" );
document.write( "fill in the distances:\r\n" );
document.write( "\r\n" );
document.write( "     Distance     Rate    Time \r\n" );
document.write( "A     8(t+.5)      8      t+.5\r\n" );
document.write( "B      10t        10       t\r\n" );
document.write( "\r\n" );
document.write( "They traveled the same distance so the\r\n" );
document.write( "two distances are equal:\r\n" );
document.write( "\r\n" );
document.write( "   8(t+.5) = 10t\r\n" );
document.write( "      8t+4 = 10t\r\n" );
document.write( "         4 = 2t\r\n" );
document.write( "         2 = t\r\n" );
document.write( "\r\n" );
document.write( "B started half an hour later than 7:30am, or\r\n" );
document.write( "8am.  2 hours later it will be 10am. \r\n" );
document.write( "\r\n" );
document.write( "Edwin
 \n" );
document.write( "
\n" );