Question

The equation $60y=390x$ represents the relationship between $x$, the time that Plane A flies in minutes, and $y$, the distance the plane flies in miles for Plane A. The graph represents the relationship for Plane B.


What is the difference in their average speed?
[Hint: Average speed = Slope of the distance-time graph $=\frac{\text{Distance traveled}}{\text{Time taken}}]$

Answer 1

Detailed step-by-step solution:
Finding the average speed of plane A:
$60y=390x$
$\Rightarrow y=\frac{390}{60}x$
$\Rightarrow y=6.5x$
Average speed of Plane A $=\frac{\text{Distance traveled}}{\text{Time taken}}$
$=\frac{y}{x}$
$=6.5$ miles/min
$=\frac{6.5x}{x}$

Finding the average speed of plane B:
Finding the slope of the graph:
Let’s consider two points $(0,0)$ and $(500,3500)$ on the graph:
$\text{Slope}=\frac{\text{Rise}}{\text{Run}}$
$=\frac{\text{Change in y}}{\text{Change in x}}$
$=\frac{3500-0}{500-0}$
$=\frac{3500}{500}$
$=7$
Average speed of plane B = Slope of the distance-time graph
$=7$ miles/min
Difference in their average speed = (Average speed of plane B) − (Average speed of plane A)
$=(7-6.5)$ miles/min
$=0.5$ miles/min
Option A is correct.