document.write( "Question 217462: Jens boat cruised 45 miles upstream and 45 miles back in a total of 8 hr. The speed of the river is 3 mph. Find the speed of the boat in still water. \n" ); document.write( "

Algebra.Com's Answer #163970 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Jens boat cruised 45 miles upstream and 45 miles back in a total of 8 hr.
\n" ); document.write( "The speed of the river is 3 mph.
\n" ); document.write( "Find the speed of the boat in still water.
\n" ); document.write( ":
\n" ); document.write( "Let s = speed in still water
\n" ); document.write( "then
\n" ); document.write( "(s+3) = speed downstream
\n" ); document.write( "and
\n" ); document.write( "(s-3) = speed upstream
\n" ); document.write( ":
\n" ); document.write( "write a time equation: Time = $\"dist%2Fspeed\"$
\n" ); document.write( ":
\n" ); document.write( "Time up + time down = 8 hrs
\n" ); document.write( " $\"45%2F%28%28s%2B3%29%29\"$ + $\"45%2F%28%28s-3%29%29\"$ = 8
\n" ); document.write( "Multiply equation by (s-3)(s+3), results
\n" ); document.write( "45(s-3) + 45(s+3) = 8(s+3)(s-3)
\n" ); document.write( ":
\n" ); document.write( "45s - 135 + 45s + 135 = 8(s^2 - 9)
\n" ); document.write( ":
\n" ); document.write( "90s = 8s^2 - 72
\n" ); document.write( ":
\n" ); document.write( "8s^2 - 90s - 72 = 0; a quadratic equation
\n" ); document.write( ":
\n" ); document.write( "Simplify, divide by 2
\n" ); document.write( "4s^2 - 45s - 36 = 0
\n" ); document.write( ":
\n" ); document.write( "Factor
\n" ); document.write( "(4s + 3)(s - 12) = 0
\n" ); document.write( ":
\n" ); document.write( "Positive solution:
\n" ); document.write( "s = 12 mph boat speed in still water
\n" ); document.write( ";
\n" ); document.write( ";
\n" ); document.write( "Check solution:
\n" ); document.write( " $\"45%2F15\"$ + $\"45%2F9\"$ = 8
\n" ); document.write( "3 + 5 = 8 hrs \n" ); document.write( "

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