A bathtub originally contains 6 gallons of water.

Question

A bathtub originally contains 6 gallons of water. A faucet is turned on and continues to fill the tub at a rate of 2 gallons per minute.

How many total gallons of water are there in the bathtub when the faucet has been on for 5 minutes?

Write an equation to represent the number of gallons of water after ‘x’ minutes after the faucet has been turned on?

Using your equation, determine how many minutes will it take until there are 38 gallons of water?

Answer 1

Hello, Nylah,

We want an equation that tells us how many gallons of water are in the bathtub as a function of time. The water is filling at a constant rate, so the equation should resemble a straight line. A good start is the familiar y = mx + b equation for a straight line, and think about what each term means. Let's assign the following:

y is the gallons of water in the bathtub.

x is the time, in minutes

m, the slope of the line, will be the rate water enters the tub (2 gallons/minute).

and b will be the starting point (there are 6 gallons already in the tub).

let's try putting these numbers into the equation and see if it makes sense.

y = 2(gal/min)*x + 6(gal)

It works for t = 0 min, since y = 6 gallons, where we started.

After 1 minute, we would expect to have 8 gallons, and the equation predicts that, since y = 2(gal/min)*1 min + 6(gal) = 8 gallons.

You can check other points to be certain this is correct. y = 2x + 6 will predict the number of gallons in the tub after x minutes (where x => 0).

To find how many minutes it takes for 38 gallons, enter the 38 for y and solve for x.

38 = 2x + 6

32 = 2X

x = 16 minutes.

I hope this helps.

Bob

Answer 2

16 gallons after 5 minutes

6+ 2(5) = 6 + 10 = 16 gallons

G= 6 + 2X

38= 6+2X

X = 16 minutes to get 38 gallons

Answer 3

To answer the two other questions, you must first create the y=mx+b question. Y will be the total gallons of water inside of the bathtub, and x will represent the minutes that passed by, and b will be the y intercept in this question which would be 6. There were 6 gallons of water initially in the bathtub before it started filling up with water.

This would be the equation= y= 2x+6

How many gallons would be in the tub after 5 minutes= y= (2)(5)+ 6

y= 16 gallons after 5 minutes

How many minutes ill it take for their to be 38 gallons? For this part we will be working backwards.

The equation we will be working with is 38= 2x+6. We will work to isolate (x)

1) 38= 2x+6

2) 32= 2x

3) x= 16

It will take 16 minutes for the tub to be filled with 38 gallons of water.