Write a direct variation equation to find the number of miles a jet travels in 3 hours if it is at the flying rate of 600mph.
Let x be the number of miles the jet travels in 3 hours.
Since the jet is traveling at a constant rate, the number of miles it travels is directly proportional to the time. Therefore, we can write a direct variation equation:
x = k * t
where k is the constant of variation and t is the time in hours.
We are given that the jet is flying at a rate of 600 mph, which means it travels 600 miles in 1 hour. Therefore, we can set up the equation as:
600 = k * 1
Solving for k:
k = 600
Substituting the value of k into the equation:
x = 600 * 3
x = 1800
Therefore, the direct variation equation to find the number of miles the jet travels in 3 hours if it is flying at a rate of 600 mph is:
x = 1800 miles.
To find the direct variation equation, we can use the formula:
y = kx
where y is the dependent variable (number of miles traveled by the jet), x is the independent variable (time in hours), and k is the constant of variation.
In this case, the jet travels at a rate of 600 miles per hour. So, when the jet flies for 1 hour (x = 1), it travels 600 miles (y = 600).
Plugging these values into the equation, we have:
600 = k(1)
Simplifying the equation, we find that k = 600.
Therefore, the direct variation equation to find the number of miles a jet travels in 3 hours, if it is at a flying rate of 600 mph, is:
y = 600x
Substituting x = 3, we can find the number of miles the jet travels in 3 hours:
y = 600(3) = 1800
Therefore, the jet will travel 1800 miles in 3 hours at a flying rate of 600 mph.
To write a direct variation equation, we need to incorporate the concept of direct variation, which states that two variables are directly proportional to each other. In this case, we have the number of miles traveled as one variable and the time taken as the other variable.
Let's denote the number of miles traveled as "m" and the time taken as "t". Since the speed of the jet is given as 600 mph, we can establish that the distance traveled is directly proportional to the time taken.
Therefore, we can express this relationship using the formula for direct variation:
m = k * t
In this equation, "k" represents the constant of variation, which remains the same for all instances of direct variation. To find the value of "k", we can use the given information that the jet travels at a rate of 600 mph for 3 hours.
Plugging in the values, we get:
600 = k * 3
To solve for "k", divide both sides by 3:
k = 600/3 = 200
Now that we have found the value of "k", we can rewrite the equation:
m = 200 * t
To find the number of miles the jet travels in 3 hours, substitute the value of 3 for "t" in the equation:
m = 200 * 3 = 600
Therefore, the direct variation equation to find the number of miles a jet travels in 3 hours, given that it is flying at a rate of 600 mph, would be:
m = 200 * t = 200 * 3 = 600 miles.