SOLUTION: An airplane flying north at the rate of 240 miles per hour passed over a flying field at noon.A second plane flying east at 200 miles per hour passed over the same field 5 minutes

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Question 369451: An airplane flying north at the rate of 240 miles per hour passed over a flying field at noon.A second plane flying east at 200 miles per hour passed over the same field 5 minutes later.When were they 250 miles apart?
Answer by amoresroy(361) About Me  (Show Source):
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An airplane flying north at the rate of 240 miles per hour passed over a flying field at noon.A second plane flying east at 200 miles per hour passed over the same field 5 minutes later.When were they 250 miles apart?
Let t = no. of minutes after 12nn that planes were 250 miles apart
Convert spped to miles per minute
240/60 = 4
200/60 = 3.333
(4t)^2 + [3.333(t-5)]^2 = 250^2
16t^2 + 11.1t^2 - 111.1t + 277.79 = 250^2
27.1t^2 - 111.1t - 62,222.2 = 0
Solve for t using the quadratic equation
t = [111.1 (+ or -)[(-111.1)^2 - 4 (27.1)(62,222.2)]^2]/(2*27.1)
We have 2 values for t:
t = 50
t = -45.9
The planes were 250 miles apart at 12:50pm & 11:14am