Question

A plane flies 525 km/hr in still air. At that rate, it can go 1200 km with a tailwind in the same time it takes to go 1000 km with a headwind. Find the rate of the wind in km/hr. Round to tenths.

Answer 1

The rate of the wind is 100 Km/h

Step-by-step explanation:

The speed of the plane is 525 Km/h, to have a tailwind is to have the rate of the wind added to your velocity. To have a headwind is to have the wind subtracted from your velocity.

We know that for a time t, the plane will travel 1200 km with tailwind and 1000 Km with headwind.

If we call the rate of the wind w, and the time it takes to travel 1200 km with tailwind and 100 km with headwind t:

`\begin{cases}525t+w={1200} \\ 525t-w={1000}\end{cases}`

Now, since we want to find w, we can use elimination to solve the system of equations. Let's subtract the second equation to the first one:

`\begin{gathered} (525t+w)-(525t-w)=1200-1000 \\ 525t-525t+w+w=200 \\ 2w=200 \\ w=(200)/(2)=100 \end{gathered}`

The rate of the wind in 100 km/h