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

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

Answer 2

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.