Question

The outside temperature decreases by 7 degrees in 3 1/2 hours. How would you represent the temperature change as a unit rate? If the temperature continues to decrease at this rate, what will the change in temperature be after 5 hours?

Answer 1

A unit rate is a rate with denominator equal to 1. So, to get that, if we have the rate 7 : 3 1/2, we can divide 7 by 3 1/2 and we will end with a unit rate.

First, let's rewrite 3 1/2 as a decimal. 1/2 is 0.5, so:

$3\frac{1}{2}=3+0.5=3.5$

So, the rate is:

$\frac{7}{3.5}=2$

Since the temperature decreases, we say it decreases by 2 degree per hour or that it changes by -2 degree per hour.

So, this means that the change in temperature is -2 degrees per hour, which is a unit rate because the denominator is 1.

To get the change in temperature after 5 hours, we can simply multiply this rate by 5, since it its a unit rate now. So:

$-2\cdot5=-10$

After 5 hours, the change in temperature will be -10 degrees.