document.write( "Question 948252: The speed of the boat is 10km/h and the speed of the river is 2km/h. Travelers take the boat and want to be back to where they started in 10hours. How far should they go, before turning around \n" ); document.write( "

Algebra.Com's Answer #578806 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The speed of the boat is 10km/h and the speed of the river is 2km/h.
\n" ); document.write( "Travelers take the boat and want to be back to where they started in 10 hours.
\n" ); document.write( " How far should they go, before turning around
\n" ); document.write( ":
\n" ); document.write( "let d = the one-way distance, (the point where they return)
\n" ); document.write( ":
\n" ); document.write( "We know from the information given that:
\n" ); document.write( "10 - 2 = 8 km/h the effective speed upstream
\n" ); document.write( "and
\n" ); document.write( "10 + 2 = 12 km/h the effective speed downstream
\n" ); document.write( ";
\n" ); document.write( "Write a time equation, time = dist/speed
\n" ); document.write( ":
\n" ); document.write( "time up + time back = 10 hrs
\n" ); document.write( " $\"d%2F8\"$ + $\"d%2F12\"$ = 10
\n" ); document.write( "multiply equation by 24
\n" ); document.write( "24* $\"d%2F8\"$ + 24* $\"d%2F12\"$ = 24*10
\n" ); document.write( "cancel the denominators
\n" ); document.write( "3d + 2d = 240
\n" ); document.write( "5d = 240
\n" ); document.write( "d = 240/5
\n" ); document.write( "d = 48 km to the point where they should turn back
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Confirm this by finding the actual time each way
\n" ); document.write( "48/8 = 6 hrs
\n" ); document.write( "48/12 = 4 hrs
\n" ); document.write( "-------------------
\n" ); document.write( "total time 10 hrs
\n" ); document.write( " \n" ); document.write( "

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