Question

The speed of an elevator varies inversely with the weight it carries. If the elevator rises at 10 feet per second when it carries 400lbs, how fast will it rise when it carries 500lbs?

Answer 1

`8(ft)/(sec)`

Explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form
`y*x=k` or
`y=k/x`

Let

x-----> the speed of the elevator

y----> the weight it carries

so

`y*x=k`

Find the constant k

For x=10 ft/sec, y=400 lb

substitute

`k=10*400=4,000`

The equation is

`y*x=4,000`

Find the speed for y=500 lb

substitute in the equation

`500*x=4,000`

`x=4,000/500=8(ft)/(sec)`