document.write( "Question 218291: Trains A and B leave the same city at right angles at the same time. Train A travels 14 km/h faster than train B. After 5 h, they are 130 km apart. Find the speed of each train. \n" ); document.write( "
Algebra.Com's Answer #164480 by ankor@dixie-net.com(22740)\"\" \"About 
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Trains A and B leave the same city at right angles at the same time.
\n" ); document.write( " Train A travels 14 km/h faster than train B. After 5 h, they are 130 km apart.
\n" ); document.write( " Find the speed of each train.
\n" ); document.write( ":
\n" ); document.write( "These are slow, slow, trains!
\n" ); document.write( ":
\n" ); document.write( "Use Pythagorean: a^2 + b^2 = c^2,
\n" ); document.write( "The dist between the trains is the hypotenuse, (c) = 130 mi
\n" ); document.write( ";
\n" ); document.write( "Let s = speed of B
\n" ); document.write( "then
\n" ); document.write( "(s+14) = speed of A
\n" ); document.write( "therefore:
\n" ); document.write( "Train A dist: 5(s+14)
\n" ); document.write( "Train B dist: 5s
\n" ); document.write( ";
\n" ); document.write( "(5(s+14))^2 + (5s)^2 = (130)^2
\n" ); document.write( "(5s + 70)^2 + 25s^2 = 16900
\n" ); document.write( "FOIL
\n" ); document.write( "(25s^2 + 700s + 4900) + 25s^2 = 16900
\n" ); document.write( ":
\n" ); document.write( "50s^2 + 700s + 4900 - 16900 = 0
\n" ); document.write( ":
\n" ); document.write( "50s^2 + 700s - 12000 = 0
\n" ); document.write( "Simplify divide 50:
\n" ); document.write( "s^2 + 14s - 240 = 0
\n" ); document.write( ":
\n" ); document.write( "Use the quadratic formula:
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "In this equation: x = s; a = 1; b =14; c = -240
\n" ); document.write( "\"s+=+%28-14+%2B-+sqrt%2814%5E2+-+4+%2A+1+%2A+-240%29%29%2F%282%2A1%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"s+=+%28-14+%2B-+sqrt%28196+-+%28-960%29+%29%29%2F2+\"
\n" ); document.write( "\"s+=+%28-14+%2B-+sqrt%28196+%2B+960+%29%29%2F2+\"
\n" ); document.write( "\"s+=+%28-14+%2B-+sqrt%281156+%29%29%2F2+\"
\n" ); document.write( "The positive solution is what we want here:
\n" ); document.write( "\"s+=+%28-14+%2B+34%29%2F2+\"
\n" ); document.write( "\"s+=+20%2F2\"
\n" ); document.write( "s = 10 km/hr speed of train B
\n" ); document.write( "and
\n" ); document.write( "10 + 14 = 24 km/hr speed of train A
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this on a calc: enter \"sqrt%28%285%2A10%29%5E2+=+%285%2A24%29%5E2%29\" = 130 \n" ); document.write( "
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