Two boats head directly toward each other, one of them traveling 12 miles per hour and the other traveling 17 miles per hour. They begin at a distance of 20 miles from each other. How far apart are they one minute before they collide?

Pat
12th grade

Think of the distance between the boats. This distance is decreasing at a rate of 12 + 17 = 29 miles per hour. One minute is one-sixtieth of an hour so in one minute the distance between them changes by 29 times ¹/₆₀ = 0.4833 miles. Thus one minute before they collide they will be 0.4833 miles apart.