A plane flies out of city A traveling an average of 325 mph, and reaches city B in 3 hours 24 minutes. On the return flight there is a tail wind that increases the plane's speed so it takes only 3 hours and 15 minutes to fly back to city A from city B. What is the speed of the tail wind?

d = 325mi/h * 3.4h = 1105 miles.

Vp = 1105mi / 3.25h = 340mi/h = speed of plane.

Vw = 340mi/h - 325mi/h = 15mi/h = speed of tail wind.

To find the speed of the tailwind, we first need to calculate the actual speed of the plane.

In the first flight from city A to city B, the plane travels at an average speed of 325 mph for a total of 3 hours 24 minutes. To convert the minutes into hours, we divide 24 minutes by 60 (since there are 60 minutes in 1 hour), which gives us 0.4 hours. Therefore, the total time for the first flight is 3 + 0.4 = 3.4 hours.

Using the formula: Speed = Distance / Time, we can rearrange the equation to find the distance traveled. The distance from city A to city B is equal for both flights since it is the same route.

Distance = Speed × Time

Distance = 325 mph × 3.4 hours
Distance = 1105 miles

Now, let's calculate the speed of the plane on the return flight. In this case, the plane travels the same distance (1105 miles) but takes 3 hours 15 minutes. Converting the minutes into hours, we divide 15 minutes by 60, which gives us 0.25 hours. Therefore, the total time for the return flight is 3 + 0.25 = 3.25 hours.

Using the formula: Speed = Distance / Time, the speed of the plane on the return flight is:

Speed = 1105 miles / 3.25 hours
Speed ≈ 339.7 mph

Now, we can find the speed of the tailwind by subtracting the average speed of the plane (325 mph) from the speed of the plane on the return flight (339.7 mph).

Tailwind Speed = Speed of Return Flight - Average Speed

Tailwind Speed = 339.7 mph - 325 mph
Tailwind Speed ≈ 14.7 mph

Therefore, the speed of the tailwind is approximately 14.7 mph.

To find the speed of the tailwind, we need to first calculate the speed of the plane without the tailwind.

Let's convert the 3 hours 24 minutes to hours. We know that 1 hour is equal to 60 minutes. So, 24 minutes is equal to 24/60 = 0.4 hours. Hence, the total time taken for the first flight is 3 + 0.4 = 3.4 hours.

Now, let's calculate the speed of the plane without the tailwind. We know that the distance between city A and city B is the same for both flights.

Distance = Speed * Time

Using the formula, we can calculate the speed of the plane without the tailwind:

Speed without tailwind = Distance / Time

Since we know the distance and time for the first flight:

Speed without tailwind = Distance / 3.4

Now, let's calculate the speed of the plane on the return flight. We'll do the same conversion for 3 hours 15 minutes, which is equal to 3 + 15/60 = 3.25 hours.

Using the formula again:

Speed without tailwind = Distance / 3.25

We can compare the two speeds without the tailwind and find the difference, which will give us the speed of the tailwind.

So the speed of the tailwind = Speed without tailwind (return) - Speed without tailwind (first flight).