2 Answers

JuneT · Answer 1 · 2018-07-15T06:47:14+0000

the constant speed, or "average rate of change" is their slope.

so hmmm looking at Fred's graph, let's pick two points on the line, say 0,0 the origin and 8,2

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 0}}\quad ,&{{ 0}})\quad % (c,d) &({{8}}\quad ,&{{ 2}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{2-0}{8-0}\implies \cfrac{2}{8}\implies \cfrac{1}{4}$

now, for Sam, let's use the last two points in the table then,

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 20}}\quad ,&{{ 2(1)/(2)}})\quad % (c,d) &({{32}}\quad ,&{{ 4}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{4-2(1)/(2)}{32-20}\implies \cfrac{4-(5)/(2)}{32-20} \\\\\\ \cfrac{\quad (8-5)/(2)\quad }{12}\implies \cfrac{\quad (3)/(2)\quad }{(12)/(1)}\implies \cfrac{3}{2}\cdot \cfrac{1}{12}\implies \cfrac{1}{8}$

Nicolas NOEL · Answer 2 · 2018-07-16T15:04:27+0000

Answer:

The constant speed of Freddy is o.25 miles per minute

Constant speed of Sam is 0.125 miles per minute

Explanation:

To find the constant speed , find out the slope using any two points

Fast Freddy:

(4,1) (8,2)

To find slope apply slope formula

slope = (y_2-y_1)/(x_2-x_1) =(2-1)/(8-4) =(1)/(4)=0.25

Constant speed is 1/4

Speedy Sam:

(4,0.5) and (32,4)

slope = (y_2-y_1)/(x_2-x_1) =(4-0.5)/(32-4) =0.125

The constant speed of Freddy is o.25 miles per minute

Constant speed of Sam is 0.125 miles per minute

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