Question

An airplane travels 4362 km against the wind in 6 hours and 5322 km with the wind in the 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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Answer 1

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Let the speed of the air plane in still air be x km/hr

And the speed of the wind be y km/hr.

Then speed of the airplane going with the wind = (x + y) km/hr

and speed of the airplane going against the wind = (x - y) km/hr.

We know that,

                                 Distance = Speed × Time

                     or,     Speed = Distance
                                                Time

According to the problem,

An airplane travels 4362 km against the wind in 6 hours

x - y = 4362/6

or, x - y = 727 ----------- (1)

Again, the airplane travels 5322 km with the wind in the same amount of time i.e. 6 hours

     x + y = 5322/6

or, x + y = 887 ----------- (2)

Now add (1) and (2) we get,

 x - y =  727

 x + y =  887

2x     = 1614

or, 2x/2 = 1614/2, (Divide both sides by 2)

or, x = 807

Now substitute the value of value of x = 807 in equation (2) we get,

  807 + y = 887

-807        -807, (Subtract 407 from both sides)

          y = 80

Answer -  Rate of the plane in still air = 807 km/hr

            Rate of the wind = 80km/hr

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Answer 2

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