Question 620145


Hello, I need help in solving this problem:

A plane flew 150 kilometers with a 30 km/hr tailwind, then turned into the wind
and flew for another 65 kilometers. If the wind and the plane’s airspeed were
constant and the entire trip took 30 minutes, what was the plane’s airspeed?
(Ignore the time needed to turn the plane around).

Thank you.


Let speed of plane in still air be S
Time taken to travel 150 km, plus time taken to fly 65 km, equals entire time taken ({{{30/60}}}, or ˝ hour)

{{{150/(S + 30) + 65/(S - 30) = (1/2)}}}


300(S - 30) + 130(S + 30) = (S + 30)(S - 30) ------ Multiplying by LCD, 2(S + 30)(S – 30)


{{{300S - 9000 + 130S + 3900 = S^2 - 900}}}


{{{430S - 5100 = S^2 - 900}}}


{{{S^2 - 430S - 900 + 5100 = 0}}}


{{{S^2 - 430S + 4200 = 0}}}


(S - 10)(S - 420) = 0


S, or speed in still air = 10 (ignore as this is IMPOSSIBLE, because the wind speed CANNOT EXCEED the plane’s speed), OR


S, or speed of plane in still air = {{{highlight_green(420)}}} km/h 


I’ll leave the check up to you.


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