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Math Review of Uniform Motion Problems

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Overview

Problem-solving strategies can also be used to solve uniform motion problems that use the relationship between distance, rate, and time.  Students can first understand the problem, develop and carry out a plan, find the answer, and then check the answer.

Understand the Problem

Suppose one car leaves Calgary, Alberta, Canada traveling north at 56 kilometers per hour.  Another car leaves Calgary one hour later, on the same road, but is traveling at a speed of 84 kilometers per hour.  How far will they be from Calgary when the faster car meets the first?  This is a uniform motion problem, using the equation distance (d) = rate (r) x time (t).   In Canada, the rate of speed is measured by using the metric system, or kilometers per hour.  The question is:  How far will the cars be from Calgary when they meet?  The data; the fast car leaves 1 hour after the slow car; the slow car travels at 56 km/h; the fast car travels at 84 km/h.  Both cars start at the same place, are traveling the same distance, and going in the same direction, so that information is not relevant to the problem.

Calgary

 

Develop a Plan

Draw a diagram using the data.  The distances for both the fast car and the slow car are the same, so in this case d represents the distance traveled by both cars when they meet.  If t is the time for the fast car, then t +1 is the time for the slow car.  Therefore, there are two equations, d = 56(t +1) and d = 84t.

Find the Answer

Since there are two equivalent equations, the substitution method can be used such that 56t +56 = 84t.  Simplifying, 56 = 84t-56t = 28t, 56/28 = t, t =2, or in about 2 hours.  Now that the time is known, the distance in kilometers can be calculated using either equation. Using the second equation for the faster car, the distance is 84(2) = 168 km, another 30 km or so past Red Deer.

Check the Answer

In order to check the answer, check to see if the equations make sense. 168 is equal to 56(3), or in other words, 168=56(1 +2), and 84 (2) = 168.  Incidentally, 56 km/h is almost 35 miles an hour and 84 km/h is about 52 miles an hour.

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