Unformatted text preview: application problems. Though
systems of equations are not necessarily needed to solve these problems,3 we feel using systems is
a more intuitive approach.
Example 8.7.3. Carl decides to explore the Meander River, the location of several recent Sasquatch
sightings. From camp, he canoes downstream ﬁve miles to check out a purported Sasquatch nest.
Finding nothing, he immediately turns around, retraces his route (this time traveling upstream),
and returns to camp 3 hours after he left. If Carl canoes at a rate of 6 miles per hour in still water,
how fast was the Meander River ﬂowing on that day?
Solution. We are given information about distances, rates (speeds), and times. The basic principle
relating these quantities is:
distance = rate · time
The ﬁrst observation to make, however, is that the distance, rate, and time given to us aren’t
‘compatible’: the distance given is the distance for only part of the trip, the rate given is the speed
Carl can canoe in still water, not in a ﬂowing river, and the time given is the duration of the entire
trip. Ultimately, we are after the speed of...
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