Question

practice problems
from unit 3, lesson 4
tyler and elena are on the cross country team.
tylers distances and times for a training run are shown on the graph.

elenas distances and times for a training run are given by the equation $y=8.5x$, where $x$ represents distance in miles, and $y$ represents time in minutes.
a. calculate each runners pace in minutes per mile.
b. who ran faster during the training run? explain or show your reasoning.

Explanation:

Step1: Find Tyler's pace from graph

From the graph, when $x=1$ mile, $y=8$ minutes. So pace = $\frac{y}{x} = \frac{8}{1} = 8$ minutes per mile.

Step2: Find Elena's pace from equation

Elena's equation: $y=8.5x$. Pace = $\frac{y}{x} = 8.5$ minutes per mile.

Step3: Compare paces to find faster runner

A lower pace (minutes per mile) means faster speed. $8 < 8.5$, so Tyler is faster.

Answer:

a. Tyler's pace: 8 minutes per mile; Elena's pace: 8.5 minutes per mile
b. Tyler ran faster. A lower minutes-per-mile pace means a faster runner, and Tyler's 8 minutes per mile is less than Elena's 8.5 minutes per mile.