You and a friend are running on treadmills. you run 0.5 mile every 3 minutes and your friend runs 2 miles every 14 minutes. you both start and stop running at the same time and run a whole number of miles. what is the least possible number of miles you and your friend can run

You run 0.5 miles every 3 minutes = > 1 mile every 6 minutes. Your friend runs 2 miles every 14 minutes = > 1 mile every 7 minutes. You run a whole number of miles every number of minutes that is a multiple of 6. Your freind runs a whole number of miles every number of minutes that is a multiple of 7 Then the least possible number of miles that you both run to end at the same time is the least common factor of 7 and 6 minutes. This is 7 * 6 = 42 minutes. You will have run 42 min / (6 miles/min) = 7 miles, and your friend will have run 42 min / (7 miles/min) = 6 miles.