document.write( "Question 742105: The speed of a boat in still water is 8 km/h. It travels 60 km upstream and 60 km downstream in a total time of 16 hours. What is the speed of the stream? \n" ); document.write( "

Algebra.Com's Answer #452282 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The speed of a boat in still water is 8 km/h.
\n" ); document.write( " It travels 60 km upstream and 60 km downstream in a total time of 16 hours.
\n" ); document.write( " What is the speed of the stream?
\n" ); document.write( ":
\n" ); document.write( "Let c = rate of the current
\n" ); document.write( "then
\n" ); document.write( "(8+c) = effective speed downstream
\n" ); document.write( "and
\n" ); document.write( "(8-c) = effective speed upstream
\n" ); document.write( ":
\n" ); document.write( "Write a time equation; time = dist/speed
\n" ); document.write( ":
\n" ); document.write( "Time upstr + time down = 16 hrs
\n" ); document.write( " $\"60%2F%28%288%2Bc%29%29\"$ + $\"60%2F%28%288-c%29%29\"$ = 16
\n" ); document.write( "multiply equation by (8-c)(8+c) canceling the denominators, you have
\n" ); document.write( "60(8-c) + 60(8+c) = 16(8-c)(8+c)
\n" ); document.write( ":
\n" ); document.write( "480 - 60c + 480 + 60c = 16(64-c^2)
\n" ); document.write( ":
\n" ); document.write( "960 = 1024 - 16c^2
\n" ); document.write( ":
\n" ); document.write( "16c^2 = 1024 - 960
\n" ); document.write( "16c^2 = 64
\n" ); document.write( "c^2 = 64/16
\n" ); document.write( "c^2 = 4
\n" ); document.write( "c = $\"sqrt%284%29\"$
\n" ); document.write( "c = 2 mph is the rate of the current
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "See if that checks out, find the actual time each way
\n" ); document.write( "60/6 = 10 hrs
\n" ); document.write( "60/10= 6 hrs
\n" ); document.write( "---------------
\n" ); document.write( "total 16 hrs
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