document.write( "Question 1077949: a boat travels 70 miles and then comes back, the current was 20 mph the total trip time was 4 hours and 40 minutes, how fast was the boat traveling \n" ); document.write( "

Algebra.Com's Answer #692446 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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a boat travels 70 miles and then comes back,
\n" ); document.write( " the current was 20 mph the total trip time was 4 hours and 40 minutes,
\n" ); document.write( " how fast was the boat traveling
\n" ); document.write( ":
\n" ); document.write( "let s = speed of the boat in relation to the water
\n" ); document.write( "then
\n" ); document.write( "(s-20) = effective speed upstream
\n" ); document.write( "and
\n" ); document.write( "(s+20) = effective speed downstream
\n" ); document.write( ":]
\n" ); document.write( "Change 4 hrs, 40 min to hrs: 4 + 40/60 = 4.67 hrs
\n" ); document.write( ":
\n" ); document.write( "Write a time equation; time = dist/speed
\n" ); document.write( "Time downstream + time upstream = 4 hr 40 min
\n" ); document.write( " $\"70%2F%28s%2B20%29\"$ + $\"70%2F%28s-20%29\"$ = 4.67 hr
\n" ); document.write( "multiply equation by (s+20)(s-20), cancel the denominators
\n" ); document.write( "70(s-20) + 70(s+20) = 4.67(s-20)(s+20)
\n" ); document.write( "distribute
\n" ); document.write( "70s - 1400 + 70s + 1400 = 4.67(s^2 - 400)
\n" ); document.write( "140s = 4.67s^2 - 1866.667
\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( "0 = 4.67s^2 - 140s - 1866.667
\n" ); document.write( "Using the quadratic formula, I got positive solution
\n" ); document.write( "s = 39.977 ~ 40 mph is boat speed
\n" ); document.write( ";
\n" ); document.write( ":
\n" ); document.write( "Check this find the actual time each way
\n" ); document.write( "70/20 = 3.5
\n" ); document.write( "70/60 = 1.167
\n" ); document.write( "--------------
\n" ); document.write( "total time 4.667 hrs which is about 4 hrs and 40 min \n" ); document.write( "

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