The natural numbers themselves are a sequence4 1 2 3

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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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