Question 82933: If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph
Answer by erimir(14)   (Show Source):
You can put this solution on YOUR website! First, let us look at the task and extract some information.
- we do know that both planes travel during two hours - the time passing between 1:00 PM and 3:00 PM.
- as plane 1 travels at 150 mph, and plane 2 at 200 mph, we may calculate how far they've traveled each on their own. distance = speed * time. Plane 1 has traveled 150*2 = 300 miles. Plane 2 has traveled 200*2 = 400 miles.
To calculate how far they are from each other, we can use a simple triangle, or even better vectors (but I'll be using a triangle and Pythagoras here).
Imagine a right angled triangle, with its 90-degree base as the point of departure. One plane travels along the line going up (north), and another to the left (west). Now the line connecting these two lines is the hypotenuse, which is the distance between them. A visualisation could be as follows:
/|
/ | N
/ | O
/ | R
/ | T
/ | H
/ |
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WEST
The pythagoras rule states that  .
In this case, we'll substitute in the values given by the task.
From the calculations, we see that the distance between the planes will be 500 miles.
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