Question

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?

Answer 1

Answer:

Rate of plane in still air: 770.5 km/hr

Rate of wind: 239.5 km/hr

Step-by-step 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.

$\text{Distance}=\text{Speed}\times \text{Time}$

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:

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

$x-w+x+w=1541$

$2x=1541$

$\frac{2x}{2}=\frac{1541}{2}$

$x=770.5$

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:

$770.5-w=531$

$770.5-770.5-w=531-770.5$

$-w=-239.5$

$-1\times -w=-1\times-239.5$

$w=239.5$

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