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 are y = 35 - 2.2x and y = 1.7x

Solution:

Given that, office building has two elevators.

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

Let "x" be the number of seconds for which the elevator is descending

Therefore, for "x" seconds the descended feet is 2.2x feet

The elevator is at 4 th floor, 35 feet above ground

Therefore, from 35 feet, the elevator has descended 2.2x feet for "x" seconds

Let "y" be the final position of elevator after "x" seconds

Therefore,

y = 35 - 2.2x

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

Here, the elevator is rising at a rate of 1.7 feet per second

Therefore, for "x" seconds, the elevator has raised 1.7x feet

Here the elevator is at ground level, therefore

y = 1.7x

Thus the system of equations are y = 35 - 2.2x and y = 1.7x