Question

Ari begins painting at 12:00 noon. At 12:30 he estimates that 15.75 gallons of paint are left, and at 2:00 he estimates that 10.5 gallons of paint remain. If the paint is used at a constant rate, how many gallons of paint were there at the start of the job?

I feel dumb for not knowing how to do this, but I really need help.

Thank you!

Answer 1

he used 15.75-10.5 = 5.25 gallons of paint in 1.5 hours. That is 3.5 gal/hr

Thus, using the point-slope form of the line, if y is the amount of paint left at x hours after 12:00, then

y-10.5 = -3.5(x-2)
So, find y when x=0.

Or, knowing that he used 3.5 gal/hr, and knowing that he had 15.75 gal 1/2 hr after starting, just add half of 3.5 to 15.75.

Either way, you will find he started with 17.5 gal of paint.

Answer 2

Ok, or I could find the slope correct? Thank you!