a drivers distance varies directly as the amount of time traveled. After 6 hours, a driver had traveled 390 miles. Write a direct variation equation relating the drivers distance travled to the amount of time driving
To write a direct variation equation relating the driver's distance traveled to the amount of time driving, you need to determine the constant of variation.
In this case, the driver's distance traveled (d) varies directly with the amount of time (t) driving. Let's call the constant of variation "k".
So, we have the equation: d = kt
We know that after 6 hours, the driver had traveled 390 miles.
Substituting these values into the equation, we can solve for the constant of variation (k).
390 = 6k
Dividing both sides of the equation by 6, we find:
k = 65
Therefore, the direct variation equation relating the driver's distance traveled (d) to the amount of time driving (t) is:
d = 65t
To write a direct variation equation relating the driver's distance traveled to the amount of time driving, we can use the formula:
Distance = Constant × Time
Let's call the constant of variation "k":
Distance = k × Time
In this case, we know that after 6 hours of driving, the driver had traveled 390 miles. So we can substitute the values into the equation:
390 = k × 6
Now we solve for k by dividing both sides of the equation by 6:
k = 390 ÷ 6
k = 65
Therefore, the direct variation equation relating the driver's distance traveled to the amount of time driving is:
Distance = 65 × Time
d = kt
390 = 6k, so k = 35
d = 35t