Word problem, how to set it up

Question

An office building has two elevators. One elevator starts out on the 4th floor, 35 feet abouve ther 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 a system of equations to represent the situation

Answer 1

Let x = seconds that have gone by and let y = elevator's height in feet. Now, we'll write one equation that models the first elevator and one that models the second elevator.

 

Think about the first elevator. It is currently 35 feet up and is losing height at a rate of 2.2 feet per second. That means its equation looks like this:

 

y = -2.2x + 35

 

The -2.2x means every second, the elevator loses 2.2 feet. The 35 means, at second x = 0, the elevator was 35 feet up.

 

Now, think about the second elevator. It is currently at ground level, which presumably is 0 feet up, and it's gaining height at a rate of 1.7 feet per second. That means its equation looks like this:

 

y = 1.7x + 0

y = 1.7x

 

The 1.7x means every second, the elevator gains 1.7 feet. The 0 can be left off, since adding 0 changes nothing. At second x = 0, the elevator will still be at 0 feet.

 

So, your system of equations is:

 

y = -2.2x + 35

y = 1.7x

 

 

Just as a note, if you "solved" this system of equations (that is, if you found the x and y values that make both equations true), you would find out at what time the elevators were at the same height (x) and how high up that would be (y).