Question

An office building has two elevators. One elevator starts out on the 4th floor, 35 feet above the ground, as it's defending at a rate of 2.2 feet per second. The other elevator starts out at ground level and is rising at a rate of 1.7 feet per second. Write a system of equations to represent the situation

Answer 1

The system of equations to represent the situation are
`y = 35 - 2.2x` and
`y=1.7x.`

Explanation:

Given:

An office building has two elevators.

One elevator starts out on the 4th floor, 35 feet above the ground, as it's defending at a rate of 2.2 feet per second.

The other elevator starts out at ground level and is rising at a rate of 1.7 feet per second.

Now, to write a system of equations to represent the situation.

Let the number of seconds for which the elevator is descending be
`x\ seconds.`

So, the descended feet is
`2.2x` feet for
`x\ seconds.`

As given the elevator is at 4th floor, 35 feet above ground.

Thus, from 35 feet the elevator has descended
`2.2x` feet for
`x\ seconds`.

Now, let the final position of elevator be
`y.`

So, it would be:

`y = 35 - 2.2x.`

Now, as given the other elevator starts out at ground level and is rising at a rate of 1.7 feet per second.

So, the elevator has been raised
`1.7x` feet for
`x\ seconds.`

As the elevator starts out at ground level.

Thus,
`y=1.7x.`

Therefore, the system of equations to represent the situation are
`y = 35 - 2.2x` and
`y=1.7x.`