SOLUTION: 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

Algebra ->  Finance -> SOLUTION: 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      Log On


   

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?
Also find the speed of the boat and the speed of the current.
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the boat
Let +c+ = the speed of the current
Let +t+ = time in hrs to go upstream
+5+-+t+ = time in hrs to go downstream
Let +d+ = one way distance
------------------------------------------
+s+%2B+c+=+12+
+s+-+c+=+8+
Add the equations
+2s+=+20+
+s+=+10+
and
+s+%2B+c+=+12+
+10+%2B+c+=+12+
+c+=+2+
-------------------------
Going upstream:
+d+=+%28+s-c+%29%2At+
+d+=+8t+
Going downstream:
+d+=+%28+s%2Bc+%29%2A%28+5+-+t+%29+
+d+=+12%2A%28+5-t+%29+
------------------------
+8t+=+12%2A%28+5-t+%29+
+8t+=+60+-+12t+
+20t+=+60+
+t+=+3+
and
+5+-+t+=+2+
------------------------
+d+=+8t+
+d+=+8%2A3+
+d+=+24+
You can go 24 miles upstream and must
turn back at 7 AM +3 hrs = 10 AM
------------------------------------
The speed of the boat is 10 mi/hr
The speed of the current is 2 mi/hr

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


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.

In this problem, the ratio of the upstream and downstream speeds is 8:12 = 2:3, so the ratio of times is 3:2.

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.

3 hours upstream at 8mph is 24 miles; 2 hours downstream at 12mph is 24 miles.

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.