Rate Vectors

Edna and Nancy leave the house of a common friend at the same time and walk for 4 hours. Edna walks due east at the average rate of 4 kilometers per hour and Nancy walks due north at the average rate of 3 kilometers per hour. What is the straight-line distance between them, in kilometers, at the end of 4 hours? (A) 4 (B) 5 (C) 12 (D) 16 (E) 20

Choice E Level of Difficulty E M H This problem can best be described as a rate vector problem, where the vectors that you will be drawing will have units of km/hr. This will be important later, so keep it in mind. We are told that Edna walks due east at a rate of 4 km/hr, so you would represent this with a vector (an arrow) pointing to the right. You can label it with the number 4, but remember that means 4 km/hr. Nancy walks due north at 3 km/hr, so this is represented by a vector pointing straight up, labeled with a 3 which means 3 km/hr. The two vectors should be starting from the same point. You will notice there is a 90 degree angle between the two vectors, so if you close the tips of the two vectors with a straight line, you have formed a right triangle whose hypotenuse (the side opposite the 90 degree angle) can be found from Pythagorean's Theorem, c2 = a2 + b2. Or, you can recall the special 3-4-5 right triangle. In either case, the hypotenuse will be 5, meaning 5 km/hr. Since rate times time equals distance, we have (5 km/hr)(4 hr) = 20 km, or choice E.