document.write( "Question 693284: The distance between two station is 192 k.m..How much time a train take to pass the stations the another train takes two hours more than the first.If the average speed of the second train is 16 k.m less than the first,then find out the average speed of both the trains ? \n" ); document.write( "

Algebra.Com's Answer #427432 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The distance between two stations is 192 k.m.
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\n" ); document.write( "let s = speed of the 1st train
\n" ); document.write( "How much time does a train take to pass the stations?
\n" ); document.write( " $\"192%2Fs\"$ = hrs
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\n" ); document.write( "The another train takes two hours more than the first.
\n" ); document.write( "If the average speed of the second train is 16 k.m less than the first,
\n" ); document.write( "then find out the average speed of both the trains ?
\n" ); document.write( ":
\n" ); document.write( "Write a time equation, time = dist/speed
\n" ); document.write( "2nd train time - 1st train time = 2 hr
\n" ); document.write( " $\"192%2F%28%28s-16%29%29\"$ - $\"192%2Fs\"$ = 2
\n" ); document.write( "multiply by s(s-16) to clear the denominators, resulting in:
\n" ); document.write( "192s - 192(s-16) = 2s(s-16)
\n" ); document.write( ":
\n" ); document.write( "192s - 192s + 3072 = 2s^2 - 32s
\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( "0 = 2s^2 - 32s - 3072
\n" ); document.write( "Simplify, divide by 2
\n" ); document.write( "s^2 - 16s - 1536 = 0
\n" ); document.write( "you can us the quadratic formula here, but this will factor to:
\n" ); document.write( "(s-48)(s+32) = 0
\n" ); document.write( "The positive solution is what we want here
\n" ); document.write( "s = 48 km/h, the speed of the faster train
\n" ); document.write( "you can find the speed of the slower
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