Question

The Diaz family is driving at a constant

speed on the highway so their distance
varies directly with their speed. They
traveled 17.5 miles in 15 minutes. How
far did they travel in 2 hours?
A 50 miles
B 70 miles
C 140 miles
D 262.5 miles
(17.5 times 15)

Answer 1

To solve this problem, we can use the concept of direct variation, which states that two quantities vary directly with each other if they can be expressed as y = kx, where y is the dependent variable, x is the independent variable, and k is a constant of variation.

In this case, the distance traveled is the dependent variable and the speed is the independent variable. We are given that the distance traveled is 17.5 miles when the time (or speed) is 15 minutes.

So, we can set up the proportion:

distance / time = constant

17.5 miles / 15 minutes = k

Solving for k, we get:

k = 17.5 / 15

k = 1.16667 (rounded to 5 decimal places)

Now that we have the constant of variation k, we can use it to find the distance traveled in 2 hours (which is equivalent to 2 hours * 60 minutes/hour = 120 minutes).

distance = k * time

distance = 1.16667 * 120

distance = 139.99964 miles (rounded to 5 decimal places)

So, the correct answer is C) 140 miles, as it is the closest rounded value to the calculated distance of 139.99964 miles.