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.
