A student is running a 5-kilometer race. He runs 1 kilometer every 3 minutes. Select the function that describes his distance from the finish line after x minutes. f of x equals negative one third x plus 5 f of x equals negative one fifth x plus 3 f of x equals one fifth x plus 5 f of x equals one third x plus 3

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Answer:

[tex]f(x)=-\frac{1}{3}x+5[/tex]

Step-by-step explanation:

The functions given are:

1. [tex]f(x)=-\frac{1}{3}x+5[/tex]

2. [tex]f(x)=-\frac{1}{5}x+3[/tex]

3. [tex]f(x)=\frac{1}{5}x+5[/tex]

4. [tex]f(x)=\frac{1}{3}x+3[/tex]

Since,

x is minutes and f(x) is kilometers.

Since we want distance from finish line, we know it will decrease from 5.

Since 1 km every 3 minutes, the slope of the line would be

change in 3 in x and change in 1 in y

Slope is y/x = 1/3

So the equation would be f(x) = 5 -1/3

Rearranging, this is first equation.

Answer:

f of x equals negative one third x plus 5

Step-by-step explanation:

We know that,

[tex]Speed =\frac{Distance}{Time}[/tex]

If for a student,

distance = 1 km, time = 3 minutes,

So, the speed of the student = [tex]\frac{1}{3}[/tex] km per min

Now, Distance = speed × time

Thus, the distance covered by students after x minutes = [tex]\frac{x}{3}[/tex] km,

∵ Total length of the race = 5 km,

Hence, the distance from the finish line after x minutes ( say f(x) ) = total length of the race - distance covered by students after x minutes

[tex]f(x)=5-\frac{1}{3}x[/tex]