Question

an airplane travels 2050 miles in the same time that a car travels 260 miles. If the rate of the plane in 358 miles per hour faster thann the rate of the car. Finnd the rate of each

Answer 1

The car's speed is approximately 52 mph, and the airplane's speed is approximately 410 mph, calculated by setting up an equation using the formula for speed and the given information.

Step-by-step explanation:

To solve the problem, we will use the formula for speed, which is distance divided by time. Let's denote the speed of the car as v (in miles per hour), and thus the speed of the plane will be v + 358 mph. Since they travel the same amount of time, we can set up the following equation:

Distance / Speed = Time

For the car: 260 / v = Time

For the plane: 2050 / (v + 358) = Time

Because the time is equal for both the car and the airplane, we have:

260 / v = 2050 / (v + 358)

Cross-multiplication gives us:

260(v + 358) = 2050v

Expanding the equation gives us:

260v + 93080 = 2050v

Subtracting 260v from both sides gives:

93080 = 1790v

Dividing by 1790 to isolate v:

v = 93080 / 1790

Calculating that gives us:

v ≈ 52 mph (speed of the car)

And the airplane's speed would be:

v + 358 ≈ 52 + 358

v + 358 ≈ 410 mph (speed of the plane)

Therefore, the car's speed is approximately 52 mph and the airplane's speed is approximately 410 mph.