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Make Sense and Persevere Len plans to run at least 3 miles each day to get ready for a cross-country race. One lap of the school track is 440 yards. If Len runs 10 laps each day, will he cover at least 3 miles? Explain.

Ask by Craig Newton. in the United States
Mar 12,2025

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Len runs 10 laps each day, which is 4,400 yards. Since 1 mile equals 1,760 yards, 4,400 yards is 2.5 miles. Therefore, Len does not run at least 3 miles each day.

Solución

Given that one lap is \(440\) yards and Len runs \(10\) laps, the total number of yards he runs each day is \[ 10 \times 440 = 4400 \text{ yards}. \] Since there are \(1760\) yards in one mile, we can convert the total yards to miles: \[ \frac{4400}{1760} = 2.5 \text{ miles}. \] Thus, since \(2.5\) miles is less than \(3\) miles, Len does not cover at least \(3\) miles by running \(10\) laps per day.

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The Deep Dive

To determine if Len's daily running meets his goal, we first need to convert miles to yards. There are 1,760 yards in a mile, so for 3 miles, Len needs to run at least 5,280 yards. If he runs 10 laps around a track measuring 440 yards, he would cover 4,400 yards (10 laps x 440 yards/lap). Since 4,400 yards is less than 5,280 yards, Len's daily goal isn’t met with 10 laps. If Len wants a surefire way to reach and exceed his 3-mile goal, he can adjust his run to about 12 laps, which will give him 5,280 yards precisely. Alternatively, he can mix in a few additional running segments or longer laps to spice up his routine. Finding the right balance will keep him motivated and racing toward his physical goals!

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