An airplane travels 5912 km against the wind in 8 hours and 7432 km with the wind in same amount of time. What is the rate of the plane in still air and what is the rate of the wind?

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Let the speed of the airplane be x km/hr and the speed of the wind be y km/hr.

Speed of the plane with the wind=x+y km/hr

Speed of the plane against the wind =x-y km/hr

Case 1(With the wind)

Speed=x+y kmph

Time =8 hr

Distance=Speed*Time =8(x+y) =7432

x+y=929 .....eqn(1)

Case 2

Speed against the wind =x-y kmph

Time taken =8 hour

Distance=Speed*Time =8(x-y)=5912

x-y=739 ...eqn(2)

Solving the system using elimination,eqn(1)+eqn(2),eliminate y

2x=739+929

x=834 kmph(answer)=>Speed of the plane

Speed of the wind=929-834 kmph=95 kmph(answer)

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