document.write( "Question 1194880: A motorboat can maintain a constant speed of 46 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 48 ​minutes; the return trip takes 44 minutes. What is the speed of the​ current \n" ); document.write( "
Algebra.Com's Answer #827172 by math_tutor2020(3835)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Upstream = against the current (the boat is slowed down)
\n" ); document.write( "Downstream = with the current (the boat is sped up)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "c = speed of the current
\n" ); document.write( "46-c = speed of the boat going upstream
\n" ); document.write( "46+c = speed of the boat going downstream
\n" ); document.write( "speeds are in mph\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "48 minutes = 48/60 = 4/5 hour
\n" ); document.write( "44 minutes = 44/60 = 11/15 hour\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Upstream:
\n" ); document.write( "distance = rate*time
\n" ); document.write( "d = r*t
\n" ); document.write( "d = (46-c)*(4/5)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Downstream:
\n" ); document.write( "d = r*t
\n" ); document.write( "d = (46+c)*(11/15)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Equate the two right hand sides and solve for c.
\n" ); document.write( "(46-c)*(4/5) = (46+c)*(11/15)
\n" ); document.write( "12(46-c) = 11(46+c)
\n" ); document.write( "552-12c = 506+11c
\n" ); document.write( "-12c-11c = 506-552
\n" ); document.write( "-23c = -46
\n" ); document.write( "c = (-46)/(-23)
\n" ); document.write( "c = 2
\n" ); document.write( "In the second step, I multiplied both sides by 15 to clear out the denominators.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Answer: The current has a speed of exactly 2 mph.
\n" ); document.write( " \n" ); document.write( "
\n" );