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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?

Verified Answer :

maryssafreimark

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.

TaeKwonDoIsDead

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

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