Boat Crossing River, Lake

Date: 8/3/96 at 23:12:49
From: Y. Samarasekera
Subject: Boat Crossing River, Lake

Dear Dr. Math,

Please help!  I have no idea how to do this problem.

Points A and B are on the banks of a river.  It takes a motorboat one 
hour to go downstream from A to B, and 1 hour 30 mins to go upstream 
from B to A.  How long would it take the motorboat to go between  
points C and D on the shore of a lake if the distance between C and D 
is the same as that between A and B?

Thank you.

Tanya

Date: 8/4/96 at 8:26:44
From: Doctor Anthony
Subject: Re: Boat Crossing River, Lake

In this type of problem you must have letters to represent the various 
unknowns; then you can write down equations to represent the 
information given.

Let x = distance A to B
Let u = speed of current of the river
Let v = speed of boat in still water.

Now using the equation:  time = distance/speed    we have 

For downstream time    x/(v+u) = 1  ........(1)

For upstream time      x/(v-u) = 1.5 .......(2)

For time on the lake we must find x/v

From (1)  x = v+u     From (2) x = 1.5v - 1.5u

We must eliminate u from these two equations

Multiply (1) by 1.5     1.5x = 1.5v + 1.5u
      and (2) gives        x = 1.5v - 1.5u
                       ---------------------
          adding        2.5x = 3v

                         x/v = 3/2.5
 
                             = 1.2 hours

                             = 1 hour 12 minutes.
 
-Doctor Anthony,  The Math Forum
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