9.ELEVATORS An office building has two elevators. One elevator starts out on the 4th floor, 35 feet above the ground, and is descending 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 and solve a system of equations to determine when both elevators will be at the same height. Interpret the solution.

To solve this problem, we can set up a system of equations based on the heights of the two elevators over time. Let's denote \( t \) as the time in seconds. For the first elevator (descending from the 4th floor): \[ h_1 = 35 - 2.2t \] For the second elevator (ascending from ground level): \[ h_2 = 1.7t \] To find when both elevators are at the same height, we set these two equations equal to each other: \[ 35 - 2.2t = 1.7t \] Now, let's solve for \( t \): \[ 35 = 1.7t + 2.2t \] \[ 35 = 3.9t \] \[ t = \frac{35}{3.9} \approx 8.97 \text{ seconds} \] Now, to find the height at that time, we can substitute \( t \) back into either equation. Using the second equation: \[ h_2 = 1.7 \times 8.97 \approx 15.4 \text{ feet} \] Thus, both elevators will be at the same height of approximately 15.4 feet after about 8.97 seconds. In context, this means that after this time, if you're waiting for the elevator on the ground floor, the first elevator which was descending will coincide with the second elevator that started rising from ground level.