SOLUTION: A search plane takes off from an airport at 6:00 AM and travels due north at 300 miles per hour. A second plane leaves the airport at the same time and travels due east at 200 mile

Question 972371: A search plane takes off from an airport at 6:00 AM and travels due north at 300 miles per hour. A second plane leaves the airport at the same time and travels due east at 200 miles per hour. The planes carry radios with a maximum range of 500 miles. When (to the nearest minute) will these planes no longer be able to communicate with each other.

Found 2 solutions by josgarithmetic, Boreal:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
RT=D and a right triangle.

t, time in hours.

t=1.387 hours or 1 hour 23 minutes 13 seconds.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
They are traveling along two legs of a right triangle with the hypotenuse being the closest distance between them.
500^2=250,000
(300x)^2 +(200x^2)=250,000
90,000 x^2 + 40,000 x^2=250,000
130,000X^2=250,000
x^2=1.923
x=1.38 hours rounding eight places to 84 minutes (being nearest minute they won't be able).
Check:
Plane A in 84 minutes will travel 420 miles
Plane B in 84 minutes will travel 280 miles
420^2=176,400
280^2=78,400
sum is 254800
check 83 minutes
415^2 + 276.677^2=248,975
84 minutes.
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