Question

A tub filled with 50 quarts of water empties at a rate of 2.5 quarts per minute. let w = quarts of water left in the tub and t = time in minutes. choose the correct answers. which equation models the relationship? is there a viable solution when time is 30 minutes?

Answer 1

Which equation models the relationship? Answer: w=50-2.5t

Is there a viable solution when time is 30 minutes? Answer: No, the tub will be empty by then.

Answer 2

This is a linear relationship. The slope-intercept form of the linear equation is:

`y=mx+c`

Where,

• m is the rate of change (positive if increasing rate and negative if decreasing rate)
• c is the y intercept, or the initial value

Rate of change is 2.5 quarts per minute (it is decreasing so m is -2.5)

Initial value is 50 quarts, so c is 50.

Plugging in the values we get
`y=-2.5x+50`.

Changing variables to w instead of y and t instead of x, gives us,

`w=50-2.5t`. Where w is warts of water left in the tub and t is the time in minutes.

There is no viable solution when t=30 because at t=20, w=0 (
`0=50-2.5(20)`). It means after 20 minutes, there is no water left. So t=30 minutes doesn't make sense.

ANSWER:

Modelling equation:
`w=50-2.5t`

When
`t=30`, there is no VIABLE solution