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.

Question

anonymous · Answer

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

anonymous · Answer

@phi?

phi · Answer

I guess they are saying let x be the time in minutes
At the beginning of the race (at time x=0) he has to run 3 km

if you replace x with 0 in the first choice
$$ f(x) = -\frac{1}{3}x + 2$$
what do you get ?

anonymous · Answer

You get 2. :)

phi · Answer

and that means the first equation means:  at the start of the race he has to run 2 km

But we know the race is 3 km.

In other words,  choice A is wrong.

phi · Answer

For the same reason, the choice D is also wrong.

anonymous · Answer

So is it B? :)

phi · Answer

It has to be B or C

to figure out which,  we use common sense.  After running for 2 minutes, the distance from the finish line should be less (he is getting closer)

in other words, if we replace x with 2, in equation B we get
$$ f(x) = -\frac{1}{2}2 + 2 = -1+2 = 1$$

in choice C we get
$$ f(x) = \frac{1}{2}2 + 2= 1+2 =3 $$

phi · Answer

which equation gives a reasonable number for  his distance from the finish line.

anonymous · Answer

C? Because he is running a 3 kilometer race? :)

phi · Answer

no.  You want
the function that describes his distance from the finish line

in other words,  an equation that tells you how far away he is from the finish line.
after running (toward the line), he gets closer.  the distance from the line gets less.

anonymous · Answer

Ohhh...I get it. So it is B :)

phi · Answer

yes

anonymous · Answer

Thank you thank you thank you! Now I get it. :)

phi · Answer

yw

anonymous · Answer

:D