document.write( "Question 943502: A motorboat, whose speed is 24 km/h in still water, takes 1 hour more to
\n" ); document.write( "go 32 km upstream than to return downstream to the same spot. Find the
\n" ); document.write( "speed of the stream
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Algebra.Com's Answer #575231 by ankor@dixie-net.com(22740)\"\" \"About 
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A motorboat, whose speed is 24 km/h in still water, takes 1 hour more to
\n" ); document.write( "go 32 km upstream than to return downstream to the same spot.
\n" ); document.write( " Find the speed of the stream
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\n" ); document.write( "let c = the rate of the stream current
\n" ); document.write( "then
\n" ); document.write( "(24+c) = the effective speed of the boat downstream
\n" ); document.write( "and
\n" ); document.write( "(24-c) = the effective speed up stream
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\n" ); document.write( "Write a time equation; time = dist/rate
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\n" ); document.write( "Time up - time down = 1 hr
\n" ); document.write( "\"32%2F%28%2824-c%29%29\" - \"32%2F%28%2824%2Bc%29%29\" = 1
\n" ); document.write( "Multiply by (24-c)(24+c)
\n" ); document.write( "(24-c)(24+c)*\"32%2F%28%2824-c%29%29\" - (24-c)(24+c)*\"32%2F%28%2824%2Bc%29%29\" = 1(24-x)(24+c)
\n" ); document.write( "Cancel the denominators
\n" ); document.write( "32(24+c) - 32(24-c) = (24-c)(24+c)
\n" ); document.write( "768 + 32c - 768 + 32c = 576 + 24c - 24c - c^2
\n" ); document.write( "Combine like terms
\n" ); document.write( "64c = 576 - c^2
\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( "c^2 + 64c - 576 = 0
\n" ); document.write( "You can use the quadratic formula a=1, b=64, c=-576, but this will factor to:
\n" ); document.write( "(x+72)(x-8) = 0
\n" ); document.write( "The positive solution is all we want here
\n" ); document.write( "x = 8 km/hr is the rate of the current
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\n" ); document.write( "See if that checks out, find the actual time each way
\n" ); document.write( "Effective speeds: 16 upstream; 32 down stream
\n" ); document.write( "32/16 = 2 hrs
\n" ); document.write( "32/32 = 1 hr
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\n" ); document.write( "differ: 1 hr \n" ); document.write( "
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