Question

Zellie is taking the stairs in her building from her floor to the top of the building. After 2 minutes, she was 100 steps from the bottom floor. After 5 minutes she was 196 steps from the bottom floor.

Answer 1

Answer:

The question seems to be incomplete, so i will think that this is a linear equation, where we can find the velocity at which she moves, and also her initial position.

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case we have two points:

"After 2 minutes, she was 100 steps from the bottom floor."

this can be represented with the point: (2min, 100 steps)

" After 5 minutes she was 196 steps from the bottom floor"

This can be represented with the point (5min, 196 steps)

With this, we can find the slope of this equation:

a = (196 steps - 100 steps)/(5min - 2min) = 96steps/3min = 32 steps/min

This means that she does 32 steps in one minute.

Then we can write her positon equation as:

y = (32steps/min)*x + b

where x represents the time, and b is her initial position.

If we replace x by 2 min, and y for 100 steps, we get:

100steps = (32steps/min)*2min + b

100 steps = 64 steps + b

100 steps - 64 steps = b = 36 steps.

This means that she started to take the stairs 36 steps from the bottom floor.