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### 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?

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

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