Question

an airplane travels 5424 km against the wind in 8 hours and 6624 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?

Answer 1

The rate of the plane is 753 km/h while the rate of the wind is 75km/h

Explanation:

Here in this question, we are interested in calculating the rate of the plane in still air and the rate of the wind.

Since we do not know these rates, we shall be representing both using variables.

Let’s represent the rate of the plane in still air by x kmph while the rate of the wind be represented by y kmph

Now, for us to calculate the speed of the plane while it travels against the wind, that would be the speed of the plane in still air minus the speed of the wind.

Mathematically, that would be (x-y) kmph

Now the speed of the plane while it travels with the wind would be its speed in still air plus the speed of the wind.

Mathematically, that would be;

(x + y) kmph

From the question;

The plane journeyed 5424 km against the speed in 8 hours, this means that its speed will be 5424/8 = 678 kmph

Thus, that means;

x -y = 678 •••••••(i)

Now, traveling with the wind , its speed will be ;

6624/8 = 828 kmph

Thus;

x + y = 828 kmph •••••••(ii)

So we have two equations to solve simultaneously;

Let’s add both together;

x -y + x + y = 828+ 678

2x = 1,506

x = 1506/2

x = 753 kmph

From ii

x + y = 828

y = 828 - x

y = 828 - 753

y = 75 kmph