Question

question 10 (1 point)
(02.04 lc)
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.
○ a ( f(x)=-\frac{1}{3}x + 2 )
○ b ( f(x)=-\frac{1}{2}x + 3 )
○ c ( f(x)=\frac{1}{2}x + 3 )
○ d ( f(x)=\frac{1}{3}x + 2 )

Explanation:

Step1: Find the speed

The student runs 1 kilometer every 2 minutes, so the speed $v=\frac{1}{2}$ km/min.

Step2: Analyze the distance - time relationship

The total distance of the race is 3 kilometers. The distance $d$ from the finish - line after $x$ minutes is the total distance of the race minus the distance run in $x$ minutes. The distance run in $x$ minutes is $s = vx=\frac{1}{2}x$ km. So the distance from the finish - line $f(x)=3-\frac{1}{2}x=-\frac{1}{2}x + 3$.

Answer:

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