Question

If a track is 400 meters around, how many laps around the track would it take to run 3.1 miles? Round to the nearest tenth. (Hint: 1 foot = 0.3048) WRITE THE DIMENSIONAL ANALYSIS!!!!!!!

Answer 1

1 lap = 400 meters

Therefore, we can use something called "dimensional analysis" to convert from laps to meters. We use equivalent quantities to do so. Since 1 lap = 400 meters, we can say

1 = 400 meters / 1 lap.

This gives us a "conversion factor" between laps and meters. Since we know we have traveled 8 laps, we can multiply this by our conversion factor (which we have defined to be equal to 1!):

8 laps * 1 = 8 laps * 400 meters / 1 lap

Now we can cancel words the same way we cancel numbers in a fraction. If we have 4 / 4, we cancel the 4's and get 1. Similarly, in the above we can cancel the "lap" with the "lap" on the bottom of the fraction of the conversion factor. Then we have:

8 laps = 3200 meters