Answers:
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Explanation:
x = number of seconds that elapse
y = altitude (aka height) of the plane
The equation for plane A is
y = 20.25x+2652
because it starts off at 2652 ft in the air, and then adds on 20.25 feet per second which is what the 20.25x describes
The equation for plane B is
y = 75.5x
The y intercept is zero because plane B starts on the ground, aka height 0.
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The system of equations is
[tex]\begin{cases}y = 20.25x+2652\\y = 75.5x\end{cases}[/tex]
If we want to know when they'll reach the same height (y), then we can set the two right hand sides equal to each other and solve for x.
75.5x = 20.25x+2652
75.5x-20.25x = 2652
55.25x = 2652
x = (2652)/(55.25)
x = 48
The two planes reach the same altitude at exactly 48 seconds
That altitude is 3624 feet because
- y = 20.25*x + 2652 = 20.25*48+2652 = 3624
- y = 75.5*x = 75.5*48 = 3624
Notice I plugged x = 48 into each equation and I got the same y value of y = 3624. This helps confirm the answers.
