If a car travels at a constant speed, the amount of gas it consumes varies directly with the distance the car travels. When a certain car travels at a constant speed of 60 miles per hour, it uses 2 gallons of gas every 50 miles. How many gallons of gas would the car use if it traveled 200 miles at a constant speed of 60 miles per hour?

$\frac{1}{2}$ gallon

$\frac{3}{4}$ gallon

4 gallons

8 gallons

12 gallons

**Solution:**

We can let g represent the number of gallons of gas the car consumes and d represent the distance the car travels. Since we are told that the amount of gas consumed by a car traveling at constant speed varies directly with the distance traveled, we can create the equation g = kd.

We are given that a car traveling at a constant speed of 60 miles per hour uses 2 gallons of gas every 50 miles. Thus, we can plug g = 2 and d = 50 into the above equation to determine k:

$\begin{array}{l}\Rightarrow g=kd\\ \Rightarrow 2=50k\\ \Rightarrow k=\frac{2}{50}=\frac{1}{25}\end{array}$

Now that we know the value of k for this car, the direct variation equation for this problem is $g=\frac{1}{25}d$. We now can determine the amount of gas the car would consume if it traveled 200 miles at a constant rate of 60 mph.

$\begin{array}{l}\Rightarrow g=\frac{1}{25}d\\ \Rightarrow g=\frac{1}{25}\times 200\\ \Rightarrow g=8\end{array}$

The car would consume 8 gallons of gas. Note that we did not plug 60 miles per hour into our direct variation equation at any point; that information in the question served only to inform us that the car is traveling at a certain constant speed.

**Alternate Solution:**

We are told that when a certain car travels at a constant speed of 60 miles per hour, it uses 2 gallons of gas every 50 miles, and we are asked how much gas the car will consume if it instead travels 200 miles at 60 miles per hour. In other words, we are increasing the number of miles traveled by a factor of 4:

$\Rightarrow 50\times 4=200$

We are also told that if a car travels at a constant speed, the amount of gas it consumes varies directly with the distance it travels. Thus, because the distance is increasing by a factor of 4, the gallons of gas consumed will increase by a factor of 4 as well:

$\Rightarrow 2\times 4=8$

The car will consume 8 gallons of gas if it travels 200 miles at a constant speed of 60 miles per hour.