Determine the equation that can help solve the problem: An airplane moving at a constant airspeed takes as long to go 450 miles with the wind as it does to go 375 miles against the... Determine the equation that can help solve the problem: An airplane moving at a constant airspeed takes as long to go 450 miles with the wind as it does to go 375 miles against the wind. Find the plane's speed in still air if the wind speed is 20 miles per hour. Let x be the plane's speed in still air. What is the speed of a car if an increase of 15 kph saves 40 minutes in covering 200 km? Let x be the car's speed. How long will it take Joshua to wash the tricycle if Bimby leaves him alone? An inlet pipe can fill a water tank in 8 minutes. Its outlet pipe can completely drain it in 10 minutes. How long would it take to fill the water tank if both pipes were left open? Read more

Steps to Solve

1. Define Variables and Setup Equations

Let $x$ be the plane's speed in still air. The plane's effective speed with the wind is $x + 20$ miles per hour, and against the wind, it's $x - 20$ miles per hour.

2. Set Up Time Equations

The time taken to travel with the wind and against the wind can be expressed as:

• Time with the wind: $\frac{450}{x + 20}$
• Time against the wind: $\frac{375}{x - 20}$

Since the time taken in both cases is the same, we set these equations equal to each other:

$$ \frac{450}{x + 20} = \frac{375}{x - 20} $$

3. Cross-Multiply to Eliminate Fractions

Cross-multiplying gives us:

$$ 450(x - 20) = 375(x + 20) $$

4. Expand and Simplify the Equation

Distributing both sides results in:

$$ 450x - 9000 = 375x + 7500 $$

Now, isolate $x$ by moving all terms involving $x$ to one side and constants to the other:

$$ 450x - 375x = 7500 + 9000 $$

$$ 75x = 16500 $$

5. Solve for x

Dividing both sides by 75 gives:

$$ x = \frac{16500}{75} $$

So,

$$ x = 220 $$

6. Final Answer

The speed of the plane in still air is 220 miles per hour.