A clogged bathtub drains at a constant rate. The amount of water in the bathtub changes by -3.75 gallons in one hour. What is the change in the amount of water in the bathtub after [tex]\frac{1}{3}[/tex] of an hour?



Answer :

To solve the problem, let's follow the steps:

1. Understand the rate of change:
The rate at which the water drains from the bathtub is given as [tex]\(-3.75\)[/tex] gallons per hour. This negative value indicates that the water level is decreasing.

2. Determine the length of time:
We need to find out the change in the amount of water after [tex]\(\frac{1}{3}\)[/tex] of an hour.

3. Calculate the change in the amount of water:
Since the water drains at [tex]\(-3.75\)[/tex] gallons per hour, we need to multiply this rate by the time period to find the total change. The calculation will be:
[tex]\[ \text{Change in water} = \text{Rate of change} \times \text{Time} \][/tex]
Substituting the given values:
[tex]\[ \text{Change in water} = -3.75 \text{ gallons per hour} \times \frac{1}{3} \text{ hour} \][/tex]

4. Perform the multiplication:
[tex]\[ \text{Change in water} = -3.75 \times \frac{1}{3} \][/tex]

5. Simplify the expression:
When you perform the multiplication:
[tex]\[ \text{Change in water} = -1.25 \text{ gallons} \][/tex]

Therefore, the change in the amount of water in the bathtub after [tex]\(\frac{1}{3}\)[/tex] of an hour is [tex]\(-1.25\)[/tex] gallons. This means that 1.25 gallons of water has drained from the bathtub in that time span.