document.write( "Question 800757: a train leaves station M and travels west at 35 km/hr. one hour later a faster train leaves station M and also travels west on a parallel track at 40 km/hr. How far from the station M will the faster train catch the slower one? \n" ); document.write( "
Algebra.Com's Answer #483278 by Edwin McCravy(20056)![]() ![]() You can put this solution on YOUR website! a train leaves station M and travels west at 35 km/hr. one hour later a faster train leaves station M and also travels west on a parallel track at 40 km/hr. How far from the station M will the faster train catch the slower one? \n" ); document.write( " \r\n" ); document.write( "There are two ways to do it, without algebra, and with algebrs:\r\n" ); document.write( "\r\n" ); document.write( "Method 1; Without algebra:\r\n" ); document.write( "\r\n" ); document.write( "You can do it this way in you head. When the faster train starts an \r\n" ); document.write( "hour after the slower train left, the slower train has 35 km head start.\r\n" ); document.write( "The faster train's catch-up rate is the difference in their speeds, or \r\n" ); document.write( "40-35 or 5 km/hr. So to catch up the entire 35 km at 5 km/hr will take \r\n" ); document.write( "7 hrs. \r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "Method 2: With algebra.\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( "-------------------------------------------\r\n" ); document.write( "Slower train \r\n" ); document.write( "Faster train \r\n" ); document.write( "\r\n" ); document.write( "Put in the speeds:\r\n" ); document.write( "\r\n" ); document.write( " Distance Rate Time\r\n" ); document.write( "-------------------------------------------\r\n" ); document.write( "Slower train 35\r\n" ); document.write( "Faster train 40 \r\n" ); document.write( "\r\n" ); document.write( "Let t = the time it takes the faster train to catch\r\n" ); document.write( "the slower train:\r\n" ); document.write( "\r\n" ); document.write( " Distance Rate Time\r\n" ); document.write( "-------------------------------------------\r\n" ); document.write( "Slower train 35 \r\n" ); document.write( "Faster train 40 t\r\n" ); document.write( "\r\n" ); document.write( "Then since the slower train travels 1 hour more than\r\n" ); document.write( "the faster train, we put t+1 for the time of the slower \r\n" ); document.write( "train:\r\n" ); document.write( "\r\n" ); document.write( " Distance Rate Time\r\n" ); document.write( "-------------------------------------------\r\n" ); document.write( "Slower train 35 t+1\r\n" ); document.write( "Faster train 40 t\r\n" ); document.write( "\r\n" ); document.write( "Use Distance = Rate × time to indicate the multiplication\r\n" ); document.write( "of the rate times the time.\r\n" ); document.write( "\r\n" ); document.write( " Distance Rate Time\r\n" ); document.write( "-------------------------------------------\r\n" ); document.write( "Slower train 35(t+1) 35 t+1\r\n" ); document.write( "Faster train 40t 40 t\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "Both trains had traveled the same distances when\r\n" ); document.write( "the faster one catches the slower one. So we\r\n" ); document.write( "set the two distances equal:\r\n" ); document.write( "\r\n" ); document.write( " 35(t+1) = 40t\r\n" ); document.write( "35t + 35 = 40t\r\n" ); document.write( " 35 = 5t\r\n" ); document.write( " 7 = t\r\n" ); document.write( "\r\n" ); document.write( "Answer: 7 hours.\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |