Question

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?

Answer 1

20 minutes, 240 barrels

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.

Answer 2

20 minutes; 240 barrels

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