Math Applications for Living I

I’ll be sharing some applications that you might find interesting from the Math119 class that I am teaching this semester. The title of this class is “Math – Applications for Living”, and that will tend to be the title of the post; this is number I in this ‘series’.

Here is the problem: You are figuring out if it makes more sense to take a bath or take a shower, in terms of conserving money or energy (or both!). The approximate dimensions of the bath tub are 6 feet by 3 feet by 2.5 feet, and you guess that it is filled halfway. Your shower head, according to the manufacturer, has a flow rate of 1.75 gallons per minute; you guess that you take 10 minutes with the shower with the water running.

A key step in solving the problem is being able to convert from cubic feet to gallons (or the reverse). In our class, we focus on flexible use of fractions — proportional reasoning. For this problem, we have the fact listed that there are 7.5 gallons in one cubic foot. If you want the values, this bath scenario uses about 170 gallons of water while the shower uses about 17.5 gallons. [We have not covered precision and significant digits yet, so I did not worry about whether they rounded the bath volume correctly.]

0.5 * (6ft * 3ft * 2.5ft) = 22.5 ft³; 22.5 ft³ * (7.5 gal/1 ft³) = 168.75 gal [Bath] 10 min * (1.75 gal/1 min) = 17.5 gal

The students were a bit surprised by the magnitude of the difference, and they seem to be getting more skilled at using these fractions. We will see how they do next week when I give them a more challenging follow-up problem.

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