A bathtub contains 45 gallons of water and the total weight of the tub and water is approximately...

Question:

A bathtub contains 45 gallons of water and the total weight of the tub and water is approximately 760.725 pounds. You pull the plug and the water begins to drain. Let v represent the number of gallons of waters that has drained from the tub since the plus was pulled. Noe that water weighs 8.345 pounds per gallon.

a. Write an expression in terms of v that represents the weight of the water that has drained from the tub (in pounds).

b. Write an expression in terms of v that represents the total weight of the tub and water (in pounds).

c. How much does the tub weight when there is no water in it?

d. If the weight of the tub and water is 618.41 pounds, how many gallons of water are in the tub?

Algebraic Expressions

In this question, we form algebraic expressions at each step to solve the question. When an expression is equated to a value, we have an equation as well.

a) The weight of the water that must have drained out will be the product of the quantity of water that has drained out (v gallons) and the weight of water per gallon (8.345 pounds). This is:

$$8.345v$$

b) The total weight when v gallons have drained out will be the difference between the initial weight and the weight that has reduced. So,

$$760.725-8.345v$$

c) When there is not water, the amount of water that must have been drained is v=45 gallons. So, the weight of the tub is:

$$760.725-8.345*45=385.2\text{ pounds}$$

d) First, let's find the amount of water that must have drained out by solving the following equation.

\begin{align} 760.725-8.345v&=618.41\\ -8.345v&=618.41-760.725\\ v&=\frac{142.315}{8.345}\\ &=17.05 \end{align}

If 17.05 gallons has drained out, the amount remaining is {eq}45-17.05=27.95\text{ gallons} {/eq}.