**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.

**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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