In a paint factory, an old conveyer line has filled 12 barrels of paint, and is filling more at a rate of 4 barrels per minute. A worker just switched on a newer line that can fill 10 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?

Step-by-step explanation:

First line is filling at 4 barrels a minute and has already filled 12

Second line is filling at 10 barrels a minute.

Assume the time taken to be equal is x:

12 + 4x = 10x

12 = 10x - 4x

6x = 12

x = 12/6

x = 2 minutes

Each barrel would have filled:

= 10x

= 10 * 2

= 20 barrels

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.