Rowing Upstream and Down

Date: 5/9/96 at 0:38:9
From: Beverly Kay Cash
Subject: Distance problems

Here is the problem.  Karen can row a boat 10 kilometers per hour in 
still water.  In a river where the current is 5 kilometers per hour, 
it takes her 4 hours longer to row x kilometers upstream than the same 
distance downstream.  Find x.

Here is what I have so far.

                d                r                 t  
downstream      x              10kph               x
                                                _________
                                                 10 kph


upstream        x             10k/4hrs             x
                              .25kph            ________
                                                .25kph

What do I do with the 5kph and how do I set it up to solve it?     

Date: 10/17/96 at 8:20:21
From: Doctor Jerry
Subject: Re: Distance problems

Dear Beverly,

I think we must assume that the x kilometers upstream is measured 
relative to the bank. So, we must calculate rates relative to the 
bank. When Karen is rowing upstream, her rate is 10 - 5 = 5, relative 
to the bank. Your analysis above, in the table, is well laid out, but 
the values under r don't take into account the "relative to the bank" 
idea. What is her rate downstream?

If you recalculate the rates, you will have used the 5kph. If you let 
Tu be the time upstream and Td the time downstream, then, since the 
distances are the same, you can equate Ru*Tu and Rd*Td.  This gives a 
relation between Tu and Td. Finally, you know something about the 
difference of the times. This will give an equation.

One final thought. If you are on a bus, which is zooming down the 
highway at 100kph, and walk at 5kph towards the front of the bus, you 
are moving at 105kph relative to the highway. Right?

I hope this answers your questions.

-Doctor Jerry,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/