I need it fast, I'm timed

It is B

Step-by-step explanation:

Plug each value possible into the equation

(48+x) / 31   =    x/15

If both sides are equal when you plug x in, it's correct

If they aren't equal, it is wrong.

How did I get this equation?

Lets use proportions to solve.

Since they are similar, (the two triangles are similar, meaning that they have the same ratio of the y and x axis values) you can use proportions meaning you make it so x over 15 is equal to the total length by the total bottom length.

If you plug 45 in as x, you get (48 + 45) divided by 31 is equal to 45/15

If you simplify the equation, you get 93 divided by 31 is equal to 3, of which 93 divided by 31 is 3

I think you know that 3=3

so it is correct.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."