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The
Two Elevators
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Strategies and Hints
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The speed of a moving object can be represented by the slope of a line where the vertical displacement is the distance travelled 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.
-
The dotted line starting from the left vertex represents the average speed of the elevator for the two trips.
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The variables
and 
can be replaced with d and 
,
respectively. - The
dotted lines at the right of the figure complete the triangle to show
that the unknown speed is the ratio of 2d to
.
Solution
The
slope of the dotted line is found by simplifying the expression 
.
This results in a speed of 
feet per second. Changing this to feet per minute yields 90 ft/min,
the solution to the problem.
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