document.write( "Question 1109199: You are at a river resort and rent a motor boat (for 5 hours) at 7am. You are told that the boat will travel 8mph upstream and 12mph downstream . You decided that you would like to go as far up river as you can, and still be back at noon. How far from the resort will you be when you turn back? What time should you turn back?
\n" ); document.write( "Also find the speed of the boat and the speed of the current. \n" ); document.write( "

Algebra.Com's Answer #724227 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "In many problems like this, a fast way to the answer is to note that, for a fixed distance, the ratio of speeds is the reciprocal of the ratio of times.

\n" ); document.write( "In this problem, the ratio of the upstream and downstream speeds is 8:12 = 2:3, so the ratio of times is 3:2.

\n" ); document.write( "If the ratio of the times at the two speeds is 3:2 and the boat is rented for 5 hours, then you should go upstream for 3 hours and downstream for 2.

\n" ); document.write( "3 hours upstream at 8mph is 24 miles; 2 hours downstream at 12mph is 24 miles.

\n" ); document.write( "So you can go 24 miles upstream from the resort before you turn back; that takes 3 hours, so if you started at 7am you need to turn around and head back at 10am. \n" ); document.write( "

\n" );