Assume that the stopping distance of a van varies directly with the square of the speed. A van traveling 40 miles per hour can stop in 40 feet. If the van is traveling 44 miles per hour, what is its stopping distance?
[ (44 / 40)^2] * 40
To solve this problem, we need to use the concept of direct variation and the given information.
First, let's write down the given information:
- The stopping distance of a van varies directly with the square of the speed.
- When the van is traveling at 40 miles per hour, it can stop in 40 feet.
Now, let's set up a proportion to find the stopping distance when the van is traveling at 44 miles per hour. We can set up the proportion as follows:
(stopping distance for 40 mph) / (stopping distance for 44 mph) = (speed of 44 mph)^2 / (speed of 40 mph)^2
We can write this proportion as:
40 / x = 44^2 / 40^2
To solve for x, we need to cross-multiply and then divide:
40 * (40^2) = 44^2 * x
Now, we can solve for x:
x = (40 * (40^2)) / (44^2)
By substituting the values and performing the calculation, we can find the value of x (stopping distance for the van at 44 mph).