Need algebra help to solve a distance, rate and time problem using a system of linear equations

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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?

Nov 15th, 2015

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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


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

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

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Nov 15th, 2015

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