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Two airplanes take off from one airfield at noon. One flies due east

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Bunuel
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Two airplanes take off from one airfield at noon. One flies due east [#permalink] New post   10 Jan 2016, 08:57
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46% (02:53) correct 54% (02:29) wrong based on 100 sessions
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Two airplanes take off from one airfield at noon. One flies due east at 200 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?

A. 166
B. 332
C. 400
D. 483
E. 566
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C
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Re: Two airplanes take off from one airfield at noon. One flies due east [#permalink] New post   10 Jan 2016, 09:48
Bunuel wrote:
Two airplanes take off from one airfield at noon. One flies due east at 200 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?

A. 166
B. 332
C. 400
D. 483
E. 566



Answer C

It forms a right angled triangle. Applying Pythogorean theorem,

566^2 = 400^2 + P^2
566^2-400^2 = P^2
(566+400)(566-400) = P^2
\sqrt{(966*166)} = P
Approximating
\sqrt{(1000*160)}=P
P= 400
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Re: Two airplanes take off from one airfield at noon. One flies due east [#permalink] New post   10 Jan 2016, 13:45
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Another way to solve this is problem, is to find a relation/pattern between these speeds. GMAT does not expect you to calculate the squares, and roots. So lets assume 200 Km/hr as 1 unit. Thus 283 = 283/200 = 1.415 = Square root of 2. There we have it.

So, it's a right-angled triangle with sides 1 unit, Square root of 2 - thus the third side will be "1 Unit".

Distance travelled in 2 hrs by the plane traveling due east = 200*2 = 400 which will be equal to distance between 2 planes.
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Re: Two airplanes take off from one airfield at noon. One flies due east [#permalink] New post   15 Jan 2016, 09:36
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Bunuel wrote:
Two airplanes take off from one airfield at noon. One flies due east at 200 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?

A. 166
B. 332
C. 400
D. 483
E. 566


Hi Bunuel,
The Q can be a bit confusing..
two planes taking off and moving in a straight line, one has to assume the angles they move is constant and same ..
If I take them moving out from airport and a point at the airport as the start point, It would be that We take them moving in the same plane, something like a rocket or two car moving on two straight roads at 45 degree to each other..
Two planes travelling straight at 45 degree to each other..
it can be a triangle with one angle 45 and two sides 400 and 566..
one by looking at the choice and two numbers can realize 566= 400 \(\sqrt{2}\)..
so 566 is the hypotenuse of a right angle isosceles triangle..
so distance is the third side=400
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Re: Two airplanes take off from one airfield at noon. One flies due east [#permalink] New post   23 Apr 2020, 04:59
If one is traveling East a rate of 200mph, it arrives at 400 miles in 2 hours
Other is traveling NE a rate of 283 mph, it arrives at 566 miles in 2 hours. Most importantly we also know that the angle traveling is 45*

This is an isosceles triangle. One 45* leg is 400 miles long, so the other 45* leg (the distance between two planes) = 400 miles

IMO answer is C
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Re: Two airplanes take off from one airfield at noon. One flies due east [#permalink]
23 Apr 2020, 04:59
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