The distance Rachel has driven varies directly with how many hours she has been driving. After 2.5 hours, she has traveled 100 miles.
Question at position 3
If she has traveled 240 miles, how many hours has she been driving?
To solve this problem, we can set up a proportion.
Let x represent the number of hours Rachel has been driving.
According to the problem, the distance she has traveled (240 miles) is directly proportional to the number of hours she has been driving (x hours).
So, we can write the proportion as:
100 miles/2.5 hours = 240 miles/x hours
To solve for x, we can cross-multiply and solve for x:
100x = 2.5 * 240
100x = 600
x = 600/100
x = 6
Therefore, Rachel has been driving for 6 hours.
The distance Rachel has driven varies directly with how many hours she has been driving. After 2.5 hours, she has traveled 100 miles.
Question at position 3
3
1 point
Question at position 3
If she has traveled 240 miles, how many hours has she been driving?
If she has traveled 240 miles, how many hours has she been driving?
6
Question at position 4
4
1 point
Question at position 4
Which of the following equations best represents this situation?
Which of the following equations best represents this situation?
y=5⁄12x
y=2.5x+100
y=2.4x
y=40x
The equation that best represents this situation is y = 2.4x.
To determine how many hours Rachel has been driving when she has traveled 240 miles, we can use the concept of direct variation.
In this scenario, we know that the distance Rachel has driven varies directly with the number of hours she has been driving. This means that the ratio of distance to time remains constant.
We are given that after 2.5 hours, Rachel has traveled 100 miles. Using this information, we can set up a proportion to find the constant ratio:
(distance after 2.5 hours) / (time after 2.5 hours) = (total distance) / (total time)
Substituting the known values:
100 miles / 2.5 hours = 240 miles / x hours
To solve for x (the number of hours when the total distance is 240 miles), we can cross-multiply and solve the equation.
100 * x = 2.5 * 240
Dividing both sides by 100:
x = (2.5 * 240) / 100
x = 6
Therefore, Rachel has been driving for 6 hours when she has traveled 240 miles.