Question

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

Answer 1

f of x equals negative one third x plus 5

Explanation:

We know that,

`Speed =(Distance)/(Time)`

If for a student,

distance = 1 km, time = 3 minutes,

So, the speed of the student =
`(1)/(3)` km per min

Now, Distance = speed × time

Thus, the distance covered by students after x minutes =
`(x)/(3)` 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

`f(x)=5-(1)/(3)x`

Answer 2

`f(x)=-(1)/(3)x+5`

Explanation:

The functions given are:

1.
`f(x)=-(1)/(3)x+5`

2.
`f(x)=-(1)/(5)x+3`

3.
`f(x)=(1)/(5)x+5`

4.
`f(x)=(1)/(3)x+3`

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.