Question

unit rate
practice & problem solving
leveled practice in 7-9, solve the rate problems.

1. a horse named northern dancer won the kentucky derby with a time of exactly 2 minutes. at this constant rate, how long would it take northern dancer to run the belmont stakes?

use the unit rate.
$\frac{1.25\text{ miles} \div 2}{2\text{ minutes} \div 2} = \frac{0.625\text{ mile}}{1\text{ minute}}$
find an equivalent rate.
$\frac{\square\text{ mile} \times 2.4}{1\text{ minute} \times 2.4} = \frac{1.5\text{ miles}}{24\text{ minutes}}$
it would take northern dancer $\square$ minutes to run the belmont stakes.

Explanation:

Step1: Calculate unit speed

$\text{Unit speed} = \frac{1.25 \text{ miles}}{2 \text{ minutes}} = 0.625 \text{ miles/minute}$

Step2: Set up time equation

Let $t$ = time for 1.5 miles.
$t = \frac{\text{Total distance}}{\text{Unit speed}}$

Step3: Substitute values and solve

$t = \frac{1.5}{0.625} = 2.4 \text{ minutes}$

Answer:

2.4 minutes