In a paint factory, an old conveyer line has filled 40 barrels of paint, and is filling more at a rate of 10 barrels per minute. A worker just switched on a newer line that can fill 12 barrels per minute. In a little while, the two lines will have filled an equal number of barrels. How long will that take? How many barrels will each line have filled?

20 minutes, 240 barrels

Step-by-step explanation:

Old line: b (x) = 40 + 10x, where x is the number of minutes elapsed.

New line: b2 (x) = 12x

Equating these two functions results in

40 + 10x = 12 x, which, when simplified, comes out to

40 = 2x, or x = 20.

An equal number of barrels will have been filled after 20 minutes.

That number is b2 (20) = 12 (20) = 240, or 240 barrels.

20 minutes; 240 barrels

Step-by-step explanation:

Old line = 40 + 10t

New line = 12t

Equal when,

40 + 10t = 12t

40 = 2t

t = 20 minutes

Each line will have:

12t = 12 (20) = 240 barrels