Write a direct variation equation to find the number of miles a jet travels if it is flying at a rate of 600 mph
Let "m" be the number of miles traveled by the jet.
Let "r" be the rate at which the jet is flying, in miles per hour.
Since the number of miles traveled is directly proportional to the rate at which the jet is flying, we can write the direct variation equation as:
m = k * r
Given that the jet is flying at a rate of 600 mph, we have:
m = k * 600
The constant of variation "k" represents the proportionality constant. However, since it is not given in the problem, we cannot ascertain its value. Therefore, the equation to find the number of miles traveled by the jet is:
m = 600k
To write a direct variation equation, we need two variables that are directly proportional to each other. In this case, the variables are the number of miles traveled and the rate at which the jet is flying.
Let's denote the number of miles as "m" and the rate at which the jet is flying as "r" measured in miles per hour.
Since the rate of the jet is given as 600 mph, we can say that the equation is:
m = r
Replacing "r" with the given rate of 600 mph, the direct variation equation is:
m = 600.
To write a direct variation equation, we need to identify the two variables involved and express their relationship using the formula y = kx, where y represents the dependent variable, x represents the independent variable, and k is the constant of variation.
In this case, the dependent variable is the number of miles the jet travels, and the independent variable is the rate at which it flies (in mph). So, we can write the direct variation equation as:
miles = k * rate
Now, to determine the value of the constant of variation (k), we need a specific example. Let's say that when the rate is 600 mph, the jet travels 900 miles. With this information, we can substitute the values into the equation:
900 = k * 600
To find the value of k, we can solve for it:
k = 900 / 600
k = 1.5
Therefore, the direct variation equation to find the number of miles a jet travels if it is flying at a rate of 600 mph is:
miles = 1.5 * rate