Question

Zane is a dangerous fellow who likes to go rock climbing in active volcanoes. One time while inside a volcano, he heard some rumbling, so he decided to climb up out of there as quickly as he could. He climbed up at a rate of 4 meters per second. After 3 seconds, he was 13 meters below the edge of the volcano.

How far was Zane below the edge of the volcano when he started climbing?

In total, how long did it take Zane to reach the edge of the volcano?

Answer 1

Answer:25 meters below the edge; 6.25 seconds

Step-by-step explanation:We can represent this with a linear function in slope-intercept form.

We know the rate of change is 4, since he climbs up at 4 meters per second. We do not know the value of b, the y-intercept.

This gives us

y = 4x + b

We know that he is 13 meters below the edge after 3 seconds. Using -13 for y and 3 for x,

-13 = 4(3) + b

-13 = 12 + b

Subtract 12 from each side:

-13-12 = 12+b-12

-25 = b

This gives us the equation

y = 4x - 25

He started out 25 meters below the edge of the volcano.

To find how long it took him to reach the edge, substitute 0 in for y:

0 = 4x - 25

Add 25 to each side:

0+25 = 4x-25+25

25 = 4x

Divide both sides by 4:

25/4 = 4x/4

6.25 = x

It takes him 6.25 seconds to reach the edge.