# Math Help - Proportionality

1. ## Proportionality

Hell-o,

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 car’s stopping distance for an initial speed of $20$ miles per hour is $17$ feet, what is its stopping distance for an initial speed of $40$ miles per hour?

$\displaystyle \frac{20}{17} = \frac{40}{x}$

$\displaystyle x = \frac{680}{20}$

$\mathrm{x = 34\ feet}$

This answer is incorrect, but I realized that multiplying it by 2 gives the correct answer (68). Is this method a fluke?

2. 40=2*20

17*2=x

It will work if it is easy to see or an integer.

3. 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:

$\displaystyle \frac{20^2}{17} = \frac{40^2}{x}$

Which is the same as...

$\displaystyle \frac{400}{17} = \frac{1600}{x}$

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

4. Originally Posted by Hellbent
Hell-o,

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 car’s stopping distance for an initial speed of $20$ miles per hour is $17$ feet, what is its stopping distance for an initial speed of $40$ miles per hour?

$\displaystyle \frac{20}{17} = \frac{40}{x}$

$\displaystyle x = \frac{680}{20}$

$\mathrm{x = 34\ feet}$

This answer is incorrect, but I realized that multiplying it by 2 gives the correct answer (68). Is this method a fluke?
You've incorrectly set up your proportions.

The proportion involves the "square" of the car's speed.

$\displaystyle\frac{20^2}{17}=\frac{40^2}{x}\Righta rrow\frac{20^2}{17}=\frac{2^2\;20^2}{x}$

$\displaystyle\ x=\frac{20^2\;2^2}{20^2}17=2^2\;(17)$