Question

A student is running a 3-kilometer race. He runs 1 kilometer every 2 minutes. Select the function that describes his distance from the finish line after x minutes.

f(x) = − 1 over 3x + 2
f(x) = − 1 over 2x + 3
f(x) = 1 over 2x + 3
f(x) = 1 over 3x + 2

Please explain how you got the answer! :)

Answer 1

The speed of the student is clearly $\frac{1}{2}$ kilometer per minute.

Therefore, the distance covered by the student in x minutes will be given as $\frac{1}{2}x$ kilometers in x minutes.

Now, with each passing minute the student is getting closer and closer to the finish line which was 3 kilometers away when the race started. Thus, as the race progresses, the distance between the student and the finish line will decrease.

All the above information can be combined together to find the the function that describes the student's distance from the finish line after x minutes as:

$f(x)=3-\frac{1}{2}x$

which can be rewritten as f(x) = − 1 over 2x + 3. Thus the second option is the correct answer.