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.