Mathematics

An aeroplane flies 1680 km with a head wind in 3.5 hours. On the return trip with same wind blowing, the plane takes 3 hours. Find the plane's air speed and the wind speed.

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Let speed of aeroplane be x km/h and speed of wind be y km/h.

Speed of aeroplane in direction of wind = (x + y) km/h

Speed of aeroplane against wind = (x - y) km/h

Given, aeroplane takes 3.5 hours to go 1680 km against the wind

$\therefore \dfrac{1680}{x - y} = 3.5$

⇒ 3.5(x - y) = 1680

⇒ x - y = 480 …….(i)

Given, aeroplane takes 3 hours to go 1680 km with the wind

$\therefore \dfrac{1680}{x + y} = 3$

⇒ 1680 = 3(x + y)

⇒ x + y = 560 …….(ii)

Adding (i) and (ii) we get,

⇒ (x - y) + (x + y) = 480 + 560

⇒ 2x = 1040

⇒ x = 520.

Substituting value of x in (i) we get,

⇒ 520 - y = 480

⇒ y = 40.

Hence, speed of aeroplane = 520 km/h and speed of wind = 40 km/h.

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