Answer to the Elevator Problem
Strategies and Hints:
1. The speed of a moving object can be represented by the slope of a line where the vertical displacement is distance traveled and the horizontal displacement is the time elapsed. Thus, a triangle can be drawn for each part of the trip. Since the distance up is the same as the distance down, the heights of the two triangles are the same.
2. The dotted line starting from the left vertex represents the average speed of the elevator for the two trips.
3. The variables t1 and t2 can be replaced with d and d/3 , respectively.
4. The dotted lines at the right of the figure complete the triangle to show that the unknown speed is the ratio of 2d to (d + d/3).
Solution:
The slope of the dotted line is found by simplifying the expression:
.
This results in a speed of 1 1/2 feet per second.
Changing this to feet per minute yields 90 ft/min, which is the solution to the problem.