The amount of paint an electric paint sprayer applies varies directly with time. A sprayer is set to apply 0.5 gallon in 2.5 minutes. Write an equation that gives the amount P of paint as a function of the time T. How much paint is applied if the sprayer is operated for 20 minutes.

Here’s how I’d do it:

You know that the sprayer spews out .5 gallons in 2.5 minutes.

Figure out how much it spews in 1 minute like this:
.5 gal = 2.5 minutes
Divide both sides by 2.5 minutes
1 gal = .5 gal/2.5 minutes or .2 gallons/minute

Now, you can make t = minutes
Spew rate in gallons = .2 x t
Make sense?

Now, in 20 minutes, you just substitute t=20 and you'll get 4 gallons.

Well, well, well, time for some artistic equations! Since the amount of paint applied varies directly with time, we can use the equation P = kT, where P is the amount of paint in gallons, T is the time in minutes, and k is a constant.

Now, we know that the sprayer applies 0.5 gallons of paint in 2.5 minutes. So, we can plug those values into our equation and solve for k. Here's how it goes:

0.5 = k * 2.5

To find k, we divide both sides by 2.5:

k = 0.5 / 2.5 = 0.2

So, our equation becomes P = 0.2T.

Now, if the sprayer operates for 20 minutes, we can plug in T = 20 into our equation:

P = 0.2 * 20 = 4 gallons

Voila! The sprayer will apply 4 gallons of paint if it's operated for 20 minutes.

Now, let's hope that whoever is operating that sprayer knows their shades of paint and doesn't go overboard with polka dots or stripes!

Since the amount of paint applied varies directly with time, we can write the equation as:

P = kT

Where P is the amount of paint, T is the time in minutes, and k is the constant of variation.

To find the value of k, we can set up a proportion using the given information:

0.5 gallon / 2.5 minutes = k

Simplifying this equation, we get:

k = 0.5 / 2.5 = 0.2

So the equation that gives the amount P of paint as a function of the time T is:

P = 0.2T

To find how much paint is applied if the sprayer is operated for 20 minutes, we can substitute T = 20 into the equation:

P = 0.2 * 20 = 4 gallons

Therefore, 4 gallons of paint is applied if the sprayer is operated for 20 minutes.

To write an equation that gives the amount P of paint as a function of the time T, we can use the concept of direct variation. From the problem, we know that the amount of paint applied varies directly with time.

We are given that the sprayer applies 0.5 gallon in 2.5 minutes. This gives us the following information:

Amount of paint (P) is directly proportional to time (T)
P = kT

We can find the constant of variation (k) by plugging in the values from the given scenario:

0.5 = k(2.5)

Solving for k, we get:

k = 0.5/2.5
k = 0.2

So, the equation that gives the amount P of paint as a function of the time T is:

P = 0.2T

Now, to find the amount of paint applied if the sprayer is operated for 20 minutes, we can substitute T = 20 into the equation:

P = 0.2(20)
P = 4

Therefore, if the sprayer is operated for 20 minutes, 4 gallons of paint will be applied.