document.write( "Question 312899: Suppose a boat travels 30 miles downstream when the current is 3 mph, then travels 30 miles upstream against a 2 mph current. If the total travel time is 5 hours, what is the speed of the boat in still water? \n" ); document.write( "

Algebra.Com's Answer #223788 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Suppose a boat travels 30 miles downstream when the current is 3 mph,
\n" ); document.write( " then travels 30 miles upstream against a 2 mph current.
\n" ); document.write( " If the total travel time is 5 hours, what is the speed of the boat in still water?
\n" ); document.write( ":
\n" ); document.write( "Let s = boat speed in still water
\n" ); document.write( "then
\n" ); document.write( "(s+3) = speed downstream
\n" ); document.write( "and
\n" ); document.write( "(s-2) = speed upstream
\n" ); document.write( ":
\n" ); document.write( "Write a time equation: time = dist/speed
\n" ); document.write( ":
\n" ); document.write( "down time + up time = 5 hrs
\n" ); document.write( " $\"30%2F%28%28s%2B3%29%29\"$ + $\"30%2F%28%28s-2%29%29\"$ = 5
\n" ); document.write( "Multiply by (s+3)(s-2), results
\n" ); document.write( "30(s-2) + 30(s+3) = 5(s+3)(s-2)
\n" ); document.write( ":
\n" ); document.write( "30s - 60 + 30s + 90 = 5(s^2 + s - 6)
\n" ); document.write( ":
\n" ); document.write( "60s + 30 = 5s^2 + 5s - 30
\n" ); document.write( "Combine on the right
\n" ); document.write( "0 = 5s^2 + 5s - 60s - 30 - 30
\n" ); document.write( ":
\n" ); document.write( "5s^2 - 55s - 60 = 0
\n" ); document.write( "Simplify, divide by 5
\n" ); document.write( "s^2 - 11s - 12 = 0
\n" ); document.write( "Factor
\n" ); document.write( "(s-12)(s+1) = 0
\n" ); document.write( "positive solution
\n" ); document.write( "s = 12 mph in still water
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solution by finding the times
\n" ); document.write( "30/(12+3) = 2 hrs
\n" ); document.write( "30/(12-2) = 3 hrs
\n" ); document.write( "------------------
\n" ); document.write( "total time: 5 hrs \n" ); document.write( "

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