It will work if it is easy to see or an integer.
I'm primarily looking for alternative solutions, assuming my method wasn't a fluke
The stopping distance of a car is the number of feet that the car travels after the driver starts applying the brakes. The stopping distance of a certain car is directly proportional to the square of the speed of the car, in miles per hour, at the time the brakes are first applied. If the carís stopping distance for an initial speed of miles per hour is feet, what is its stopping distance for an initial speed of miles per hour?
This answer is incorrect, but I realized that multiplying it by 2 gives the correct answer (68). Is this method a fluke?
To quote: "The stopping distance of a car is directly proportional to the square of the speed of the car."
So the structure for your working should actually be:
Which is the same as...
When you attempted the solution, you used a number on your second fraction which was double the original amount, when in actual fact it should have 4 times. That's why you needed to multiply by 2 again to achieve the correct answer. Your method is fine, otherwise.
Hope that helps. :V