Question

Superman needs to save Lois from the clutches of Lex Luthor. After flying for 7 seconds, he is 1687 meters from her. Then at 15 seconds, he is 1215 meters from her.
What is Superman's average rate?

How far does Superman fly every 14 seconds?

How close to Lois is Superman after 29 seconds?

Answer 1

Answer:

Step-by-step explanation:

Given : Superman needs to save Lois from the clutches of Lex Luthor. After flying for 7 seconds, he is 1687 meters from her. Then at 15 seconds, he is 1215 meters from her.

To Find :

What is Superman's average rate?  

How far does Superman fly every 14 seconds?

How close to Lois is Superman after 29 seconds?

Solution :

seconds             meters

 7                          1687

15                         1215

$(x_{1},y_{1})=(7,1687)$

$(x_{2},y_{2})=( 15, 1215)$

Slope tells about the rate

Thus slope = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

              = $\frac{1215-1687}{15-7}$

             = -59

Thus  Superman's average rate is -59m/s

Every second he's 59 meters closer to Lois,

So if at 15 seconds he's 1215 meters, then the second before that he was 1215-(-59)=1215+59 =1274 meters closer.

how close is he at 29 seconds?

Since the 29 second is 14 seconds away from the 15 seconds, So, 1215 + 14(-29)

= 809 meters

Answer 2

$\bf \begin{array}{ccll} seconds&meters\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 7&1687\\ 15&1215 \end{array}\\\\ -------------------------------$

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 7}}\quad ,&{{ 1687}})\quad % (c,d) &({{ 15}}\quad ,&{{ 1215}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1215-1687}{15-7}\implies \cfrac{-472}{8} \\\\\\ \cfrac{-59}{1}\implies -59\frac{meter}{sec}\impliedby \begin{array}{llll} average\\ rate\ of\\ change \end{array}$

well, every second he's 59 meters closer to Lois, so if at 15seconds he's 1215 meters, then the second before that he was 1215+59 meters closer.

how close is he at 29 seconds? since the 29second is 14 seconds away from the 15th, just hop 14 times from the 15th second, or 1215 + 14(-29)