# Question Video: Evaluating Algebraic Expressions in a Real-World Context

One measure of distance is rate multiplied by time, 𝑑 = 𝑟𝑡. Find the distance Olivia travels if she is moving at a rate of 60 mph for 6.75 h.

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### Video Transcript

One measure of distance is rate multiplied by time, 𝑑 equals 𝑟𝑡. Find the distance Olivia travels if she is moving at a rate of 60 miles per hour for 6.75 hours.

This question refers to the rate of travel, which may also be referred to as speed. A common measure of speed or rate is miles per hour. The formula given in the question, 𝑑 equals 𝑟𝑡, is a commonly used one. It is often given in triangular form, as shown. The D stands for the distance. T stands for time. S stands for speed, which in our question has been altered to 𝑟 for rate. This leads us to three rearranged formulae. Speed is equal to distance divided by time, time is equal to distance divided by speed, and distance is equal to speed multiplied by time. It is this version of the formula that we are using in this question.

We are told that the rate or speed is 60 miles per hour. And the time is 6.75 or six and three-quarter hours. To calculate the value of 𝑑, the distance, we need to multiply 60 by 6.75. There are lots of ways of performing this calculation without a calculator. We could begin by splitting 60 into six multiplied by 10 and then multiplying 6.75 by 10. This is equal to 67.5. We could then multiply 67.5 by six using a column multiplication method. This gives us an answer of 405.0. 60 multiplied by 6.75 is 405. As our units for the rate were miles per hour and our units for time were hours, the units for distance will be miles. The distance that Olivia traveled was 405 miles.

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