Write a direct variation equation to find the number of miles a jet travels in 3 hours if it is flying at a rate of 600 mph.
Let y be the number of miles the jet travels in 3 hours.
Since the jet is flying at a rate of 600 mph, the distance it travels in one hour can be given as 600 miles.
Since distance traveled is directly proportional to time,
we can write the direct variation equation as:
y = 600 * 3
To write a direct variation equation, we can use the formula: y = kx, where y represents the dependent variable, x represents the independent variable, and k represents the constant of variation.
In this case, the number of miles traveled is the dependent variable, and the time spent flying is the independent variable. Since we want to find the number of miles traveled in 3 hours, we can set x = 3.
Given that the jet is flying at a rate of 600 mph, we can set y = 600.
Substituting these values into the equation, we get:
600 = k * 3
Simplifying the equation, we have:
600 = 3k
Now, we can solve for k by dividing both sides of the equation by 3:
600/3 = 3k/3
200 = k
Therefore, the direct variation equation to find the number of miles a jet travels in 3 hours if it is flying at a rate of 600 mph is:
y = 200x
To write a direct variation equation, we need to establish the relationship between the two variables involved. In this case, the variables are the number of miles traveled and the time taken by the jet.
We know that the jet is flying at a constant rate of 600 mph, meaning it travels 600 miles in 1 hour. So, we can say that the number of miles traveled (M) is directly proportional to the time taken (T).
The equation for direct variation can be expressed as M = kT, where M represents the number of miles traveled, T represents the time taken in hours, and k is the constant of variation.
To find the value of k, we can use the given information. If the jet is flying at a rate of 600 mph, we know that it will travel 600 miles in 1 hour. So, we can substitute the values into the equation:
600 = k * 1
This simplifies to k = 600. Now we can rewrite the equation as:
M = 600T
To find the number of miles the jet travels in 3 hours, we substitute T = 3 into the equation:
M = 600 * 3
Simplifying further, we find that the jet would travel 1800 miles in 3 hours.