Final answer:
To find out how far Dancer ran, the expression r × 1/4 mile is used, where r represents the number of laps run. Multiply the number of laps by the distance of one lap to calculate the total distance.
Step-by-step explanation:
To determine how far Dancer ran, we need to write an expression that multiplies the number of times (r) Dancer ran around the track by the distance of the track. Since the track is 1/4 mile long, and he ran r times, the expression would be r × 1/4 mile. This calculates the total distance Dancer ran.
Example Calculation
If he ran around the track 4 times, then he ran:
4 × 1/4 mile = 1 mile.
Using another example, if Dancer ran 10 laps, then he ran:
10 × 1/4 mile = 2.5 miles.
It's essential to know these calculations can be applied to study the running speed, running distance, and exercise pace of an athlete which refers to the second point mentioned: 40 percent of runners ran at speeds of 7.5 miles per hour or less.
Significant Figures
When calculating distances in athletics, it's important to consider significant figures. As seen in the provided example where a marathon runner completes various distances, the sum of the distances was reported with the correct significant figures. An algebraic approach like the one with Dancer's laps ensures precision in measurement.