document.write( "Question 774933: It takes 12 seconds for two trains to pass one another when moving in opposite directions. if they are in the same direction, it will take the faster train 3 minutes to pass the slower one. If the trains are `30 meters and 120 meters long, respectively, what are the rates of the two trains? \n" ); document.write( "
Algebra.Com's Answer #472636 by ankor@dixie-net.com(22740)\"\" \"About 
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It takes 12 seconds for two trains to pass one another when moving in opposite directions.
\n" ); document.write( "if they are in the same direction, it will take the faster train 3 minutes to pass the slower one.
\n" ); document.write( " If the trains are `30 meters and 120 meters long, respectively, what are the rates of the two trains?
\n" ); document.write( ":
\n" ); document.write( "Convert 3 min to 180 seconds
\n" ); document.write( ":
\n" ); document.write( "let a = rate of train 1, (faster)
\n" ); document.write( "let b = rate of train 2
\n" ); document.write( ":
\n" ); document.write( "towards each other
\n" ); document.write( "12a + 12b = 30 + 120
\n" ); document.write( "12a + 12b = 150 m
\n" ); document.write( ":
\n" ); document.write( "a passing b
\n" ); document.write( "180a - 180b = 150
\n" ); document.write( "Multiply the 1st equation by 15, add to the above equation
\n" ); document.write( "180a + 180b = 2250
\n" ); document.write( "180a - 180b = 150
\n" ); document.write( "---------------------Addition eliminates b, find a
\n" ); document.write( "360a = 2400
\n" ); document.write( "a = 2400/360
\n" ); document.write( "a = 6\"2%2F3\" m/sec is the speed of the 1st train, about 24 km/hr
\n" ); document.write( ":
\n" ); document.write( "Find b
\n" ); document.write( "12(6.667) + 12b = 150
\n" ); document.write( "12b = 150 - 80
\n" ); document.write( "12b = 70
\n" ); document.write( "b = 70/12
\n" ); document.write( "b = 5\"5%2F6\" m/sec is the speed of the 2nd train, about 21 km/hr \n" ); document.write( "
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