you pull out the plug from the bathtub. after 30 seconds, there are 14 gallons of water left in the tub. one minute after you pull the plug, there are 9 gallons left.

how many gallons of water were in the tub initially, that is before the plug was pulled?

how many gallons of water were still in the tub 45 seconds after the plug was pulled.

We had a very similar question yesterday

https://www.jiskha.com/display.cgi?id=1512043982

In that one, I had found the slope
Using (30,14) as a point, find the equation in the form
y = mx + b
then sub in 45 for x to get the number of gallons

To solve both of these problems, we can use the concept of rate of drainage. The rate of drainage can be determined from the information given and can help us answer the questions.

Let's start with the first question:
To find the initial amount of water in the tub before the plug was pulled, we need to calculate the rate of drainage first.

From the information given, we can deduce that the tub loses 14 gallons of water in 30 seconds, and 9 gallons in 1 minute (60 seconds).

To calculate the rate of drainage, we can divide the change in water volume by the change in time:
Rate of drainage = (Change in water volume) / (Change in time)

For the first scenario:
Rate of drainage = (14 gallons - Initial amount of water) / 30 seconds

For the second scenario:
Rate of drainage = (9 gallons - Initial amount of water) / 60 seconds

By solving these equations, we can determine the initial amount of water in the tub.

Now, let's move on to the second question:
To find the amount of water left in the tub 45 seconds after the plug was pulled, we can utilize the information we have and the rate of drainage.

Given that the tub loses 14 gallons in 30 seconds (which means the drainage rate is constant), we can calculate the amount of water lost in 45 seconds by using proportions.

Let X be the amount of water lost in 45 seconds:
14 gallons / 30 seconds = X gallons / 45 seconds

By solving this proportion, we can find X, which represents the amount of water lost in 45 seconds. Subtracting this value from the initial amount of water will give us the amount of water remaining.

Following these steps, we can work out both problems.