an airplane travels 500 km with the wind in the same time that it takes the airplane to travel 400 km against the wind. the average speed of the plane in still air is 180 km/h. what is the average speed of the wind?

Airplane with wind:
Distance: 500km
Speed: 180+x
Time:

Airplane against wind:
Distance: 400km
Speed: 180-x
Time:

I'm not sure how to do this. Can i please get help?

Thank you so much

So My equation would be:
500/180+x= 400/180-x

And the answer that I get is: 20km/h.

Is at correct?

500=(va+vw)*time

400=(va-vw)*time

500=(va+vw)(400)/(va-vw)
500(va-vw)=400(va+vw)
you are given Va=180
Can you solve it now?

I'm not sure what you did. What is VA and VW?

correct.

Why did the airplane join a comedy club? Because it wanted to learn some jokes to fly with the wind! Now, let's solve this problem together.

Let's start by finding the time it takes for the airplane to travel with the wind. We can use the formula:

Time = Distance / Speed

For the airplane with the wind, the distance is 500 km, and the speed is the average speed of the airplane in still air (180 km/h) plus the speed of the wind (let's call it x km/h). So the time it takes is:

Time = 500 km / (180 km/h + x km/h)

Now let's find the time it takes for the airplane to travel against the wind. Using the same formula:

Time = Distance / Speed

For the airplane against the wind, the distance is 400 km, and the speed is the average speed of the airplane in still air (180 km/h) minus the speed of the wind (x km/h). So the time it takes is:

Time = 400 km / (180 km/h - x km/h)

According to the problem, these two times are equal. So we can set up an equation:

500 / (180 + x) = 400 / (180 - x)

Now, let's solve this equation. I'll leave that part to you!

Of course! I can help you solve this problem.

Let's start by calculating the time it takes for the airplane to travel with the wind. We can use the formula: time = distance / speed.

For the airplane traveling with the wind:
Distance = 500 km
Speed of the plane in still air = 180 km/h + x (let's call this equation 1)

So, the time taken for the airplane to travel with the wind can be calculated as:
Time with wind = 500 km / (180 km/h + x) (equation 2)

Now, let's calculate the time it takes for the airplane to travel against the wind:
Distance = 400 km
Speed of the plane in still air = 180 km/h - x (let's call this equation 3)

So, the time taken for the airplane to travel against the wind can be calculated as:
Time against wind = 400 km / (180 km/h - x) (equation 4)

The problem states that these two times are equal. In other words:
Time with wind = Time against wind

We can put equations 2 and 4 together to solve for x, the average speed of the wind:

500 km / (180 km/h + x) = 400 km / (180 km/h - x)

To solve this equation, we can cross-multiply and solve for x:

500 km * (180 km/h - x) = 400 km * (180 km/h + x)

Solving this equation will give us the value of x, which represents the average speed of the wind.