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.

Answer 1

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.