document.write( "Question 251117: a train leaves the city heading west and travels at 50 miles per hour. Three hours later, a second train leaves from the same place and travels in the same diresction at 65 miles per hour. How long will it take for the second train to overtake the first train? \n" ); document.write( "
Algebra.Com's Answer #182869 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
a train leaves the city heading west and travels at 50 miles per hour. Three hours later, a second train leaves from the same place and travels in the same diresction at 65 miles per hour. How long will it take for the second train to overtake the first train?
\n" ); document.write( "
\r\n" );
document.write( "You can do it in your head. The first train goes 50 mph for 3 hours,\r\n" );
document.write( "so it's 150 miles from the starting point when the second train starts.\r\n" );
document.write( "The first train is 150 miles ahead of the second train, and the second \r\n" );
document.write( "train goes only 15 mph faster, so it'll take it 10 hours to catch\r\n" );
document.write( "up the 150 miles it's behind.\r\n" );
document.write( "\r\n" );
document.write( "But your teacher wants you to do it with algebra. OK\r\n" );
document.write( "\r\n" );
document.write( "Let t = the time it will take the second train to catch up.\r\n" );
document.write( "\r\n" );
document.write( "Make this chart:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                distance       rate       time\r\n" );
document.write( "first train    \r\n" );
document.write( "second train       \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let the answer be t, so fill in t for the second train's\r\n" );
document.write( "time to catch up\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                distance       rate       time\r\n" );
document.write( "first train                             \r\n" );
document.write( "second train                                t         \r\n" );
document.write( "\r\n" );
document.write( "Next fill in the two give rates of speed:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                distance       rate       time\r\n" );
document.write( "first train                     50         \r\n" );
document.write( "second train                    65          t     \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The first train travel 3 hours longer than the\r\n" );
document.write( "second train, so add 3 to the time for the the \r\n" );
document.write( "first train, getting t+3 and fill that in for\r\n" );
document.write( "the first train's time:P\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                distance       rate       time\r\n" );
document.write( "first train                     50         t+3\r\n" );
document.write( "second train                    65          t \r\n" );
document.write( "\r\n" );
document.write( "No use distance = rate x time \r\n" );
document.write( "\r\n" );
document.write( "to fill in the two distances\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                distance       rate       time\r\n" );
document.write( "first train      50(t+3)        50         t+3\r\n" );
document.write( "second train      65t           65          t \r\n" );
document.write( "\r\n" );
document.write( "Those distances must be equal when the second train \r\n" );
document.write( "catches up to overtake the first train: \r\n" );
document.write( "\r\n" );
document.write( "So the equation is \r\n" );
document.write( "\r\n" );
document.write( "          50(t+3) = 65t\r\n" );
document.write( "\r\n" );
document.write( "Solve that and you'll get t = 10 which we got doing\r\n" );
document.write( "it in our heads.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );