A\:twin\:engined\:aircraft\:can\:fly\:768\:miles\:from\:city\:a\:to\:city\:b\:in\:3\:hours\:with\:wind\:and\:make\:the\:return\:trip\:in\:8\:hours\:against\:the\:wind.\:What\:is\:the\:speed\:of\:the\:wind?\:

Let:
- \( x \) = the speed of the plane in still air (in miles per hour),
- \( y \) = the speed of the wind (in miles per hour),
- Distance from city A to city B = 768 miles.

### With the wind:
- The effective speed of the plane when flying with the wind is \( x + y \).
- The plane takes 3 hours to cover 768 miles, so:
\[
\frac{768}{x + y} = 3
\]
This simplifies to:
\[
x + y = \frac{768}{3} = 256 \quad \text{(Equation 1)}
\]

### Against the wind:
- The effective speed of the plane when flying against the wind is \( x - y \).
- The plane takes 8 hours to cover the same 768 miles, so:
\[
\frac{768}{x - y} = 8
\]
This simplifies to:
\[
x - y = \frac{768}{8} = 96 \quad \text{(Equation 2)}
\]

### Solving the system of equations:
1. From Equation 1: \( x + y = 256 \),
2. From Equation 2: \( x - y = 96 \).

Add the two equations:
\[
(x + y) + (x - y) = 256 + 96
\]
\[
2x = 352
\]
\[
x = 176
\]

Now, substitute \( x = 176 \) into Equation 1:
\[
176 + y = 256
\]
\[
y = 256 - 176 = 80
\]

Thus, the speed of the wind is **80 miles per hour**.

Would you like further details or have any questions?

### 5 Related Questions:
1. How would the time change if the wind speed increased by 10 mph?
2. What if the distance between cities was 1000 miles instead of 768?
3. How would the calculation change if the plane took 5 hours with the wind and 7 hours against it?
4. Can this method be used for calculating the speed of a boat in a river with current?
5. What would happen if there was no wind at all?

### Tip:
When solving motion problems, clearly distinguish between speeds with and against the wind or current to set up the right equations.

A twin-engined aircraft can fly 768 miles from city A to city B in 3 hours with wind and make the return trip in 8 hours against the wind. What is the speed of the wind?

Learn how to calculate the wind speed for a twin-engined aircraft flying 768 miles with wind and against wind. This problem covers algebraic concepts, such as systems of linear equations and the distance-speed-time relationship, suitable for Grades 8-10.

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