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Fyling against the wind, an airplane travels 4779 kilometers in 9 hours. Flying the same wind, the sampe plane travels 6060 kilometers in 6 hours. What is the rate of the plane still in the air abd what is the rate if the winf?

User AbiSaran
by
7.7k points

1 Answer

2 votes

Answer:

Rate of plane in still air: 770.5 km/hr

Rate of wind: 239.5 km/hr

Explanation:

Let x represent speed of plane in still air and w represent speed of wind.

Speed of plane with wind would be
x+w.

Speed of plane against wind would be
x-w.

We will use following formula to solve our given orblem.


\text{Distance}=\text{Speed}* \text{Time}

We have been given that flying against the wind, an airplane travels 4779 kilometers in 9 hours. We can represent this information in an equation as:


9(x-w)=4779...(1)


x-w=531...(1) (Dividing by 9)

We are also told that flying with the wind, the same plane travels 6060 kilometers in 6 hours. We can represent this information in an equation as:


6(x+w)=6060...(2)


x+w=1010...(2) (Dividing by 6)

Upon adding equation (1) and (2), we will get:


(x-w)+(x+w)=531+1010


x-w+x+w=1541


2x=1541


(2x)/(2)=(1541)/(2)


x=770.5

Therefore, the rate of the plane in still air is 770.5 kilometers per hour.

To find the rate of the wind, we will substitute
x=770.5 in equation (1) as:


770.5-w=531


770.5-770.5-w=531-770.5


-w=-239.5


-1* -w=-1*-239.5


w=239.5

Therefore, the rate of the wind is 239.5 kilometers per hour.

User Artfulbeest
by
8.6k points
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