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

timer Asked: Nov 15th, 2015
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Question Description

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?

Tutor Answer

School: New York University

Thank you for the opportunity to help you with your question!

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)

Please rate my answer so that I can further help you in the future.Thanks

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