Mattie Evans drove 140 miles in the same amount of time that it took tubropropellar plane to travel 500 miles. The speed of the plane was 180 mps faster than the speed of the car. Find the speed of the plane.
180 m/s = 402 mi/hr
time = distance/speed, so
500/x = 140/(x-402)
x = 558 mi/hr
You can convert that back to m/s if you want, but the mish-mash of units is just paperwork.
Let's assume the speed of the car is "x" mph.
Since Mattie Evans drove 140 miles in the same amount of time it took the plane to travel 500 miles, we can set up an equation:
Time taken by the car = Time taken by the plane
Distance / Speed for the car = Distance / Speed for the plane
140 miles / x mph = 500 miles / (x + 180) mph
Cross-multiplying the equation gives us:
140(x + 180) = 500(x)
Simplifying the equation:
140x + 25200 = 500x
Rearranging the equation:
500x - 140x = 25200
360x = 25200
Dividing by 360 on both sides:
x = 25200 / 360
Simplifying:
x = 70
So, the speed of the car is 70 mph.
To find the speed of the plane, we can substitute the value of x in the original equation:
Speed of the plane = Speed of the car + 180
= 70 + 180
= 250
Therefore, the speed of the plane is 250 mph.
To find the speed of the plane, let's assume the speed of the car is "x" miles per hour.
The time it took for the car to travel 140 miles is the same as the time it took for the plane to travel 500 miles.
For the car, we can calculate the time taken using the formula:
Time = Distance / Speed
Time taken by the car = 140 / x
For the plane, the speed is 180 miles per hour faster than the car. So, the speed of the plane is (x + 180) miles per hour.
Using the formula for time, we can calculate the time taken by the plane:
Time = Distance / Speed
Time taken by the plane = 500 / (x + 180)
Since the times are equal, we can equate the two equations:
140 / x = 500 / (x + 180)
To solve for "x," we can cross-multiply:
140(x + 180) = 500x
Expanding the equation:
140x + 25200 = 500x
Bringing all "x" terms to one side:
500x - 140x = 25200
Combining like terms:
360x = 25200
Finally, solving for "x," divide both sides by 360:
x = 25200 / 360
Calculating this:
x ≈ 70
Therefore, the speed of the car is approximately 70 miles per hour.
To find the speed of the plane, we can substitute the value of "x" into the equation:
Speed of the plane = Speed of the car + 180
Speed of the plane = 70 + 180
Calculating this:
Speed of the plane ≈ 250 miles per hour
Therefore, the speed of the plane is approximately 250 miles per hour.