9.2. Applications

Many applications contain two or more unknowns that must be found. To solve such problems, we must write as many independent equations as there are unknowns. Otherwise, it is not possible to obtain numerical answers.

Set up these problems as we did in Chap. 3, and solve the resulting system of equations by any of the methods of this chapter.

We give applications from several branches of technology, so you can find problems that apply to your field. However, you may want to try some applications outside your own field. Everything you need to tackle such problems is given in these pages. Having some familiarity with branches of technology other than your own will make you more valuable on the job.

9.2.1. Uniform Motion Applications

Recall from Chap. 3 that motion is called uniform when the speed does not change. These problems can be set up using the simple formula,


rate × time = distance

Example 14:

A delivery truck is traveling at 40 mi/h. After the truck has a 35-mile head start, a car leaves from the same place traveling at 65 mi/h, to overtake the truck. (a) How long will it take the car to overtake the truck? (b) How far from the starting point will the car overtake the truck?

Solution: Let t = time for the car to overtake the truck, in hours, and d = distance from starting point to where car overtakes truck, in miles.

  1. For each vehicle, rate × time = distance, so noting that in t hours the truck travels 35 fewer miles than the car, we write;

    Subtracting ...

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