Mattie drove 140 miles in the same amount of time that it took a tubropropeller plane to travel 520 miles. The speed of the plane was 190 mph faster than the speed of the car. Find the speed of the plane

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Let's assume that the speed of the car is x mph.

According to the given information, the time taken by Mattie to drive 140 miles is the same as the time taken by the turbo propeller plane to travel 520 miles.

Using the formula Time = Distance / Speed, we can write the equation for the car as:

Time taken by the car = 140 / x

Now, we know that the speed of the plane is 190 mph faster than the speed of the car, so we can express the speed of the plane as (x + 190) mph.

Using the formula Time = Distance / Speed, we can write the equation for the plane as:

Time taken by the plane = 520 / (x + 190)

Since both times are the same, we can set them equal to each other:

140 / x = 520 / (x + 190)

To solve for x, we can cross multiply:

140(x + 190) = 520x

140x + 26600 = 520x

Subtract 140x from both sides:

26600 = 380x

Now, divide both sides by 380:

x = 26600 / 380

x ≈ 70

Therefore, the speed of the car is approximately 70 mph.

To find the speed of the plane, add 190 mph to the speed of the car:

Speed of the plane = 70 + 190

Speed of the plane = 260 mph

Therefore, the speed of the plane is 260 mph.

To find the speed of the plane, we need to set up a system of equations based on the information given in the question.

Let's denote the speed of the car as "x" mph. Therefore, the speed of the plane would be "x + 190" mph because it is 190 mph faster.

Now, we know that the time taken by both the car and the plane is the same. We can use the formula:

Time = Distance / Speed

For the car, the distance is given as 140 miles, and the speed is "x" mph.
So, the time taken by the car = 140 / x.

For the plane, the distance is given as 520 miles, and the speed is "x + 190" mph.
So, the time taken by the plane = 520 / (x + 190).

Since the times are equal, we can set up the equation:

140 / x = 520 / (x + 190)

To solve this equation, we can cross-multiply:

140(x + 190) = 520x

Now, let's expand and simplify the equation:

140x + 26600 = 520x

Moving the terms around, we isolate the x term on one side:

520x - 140x = 26600

Combine like terms:

380x = 26600

Finally, divide both sides of the equation by 380 to find the value of x:

x = 26600 / 380

Calculating this, we find:

x ≈ 70

Therefore, the speed of the plane would be:

x + 190 = 70 + 190 = 260 mph.

Hence, the speed of the plane is 260 mph.