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 = 40 + 10t

New line = 12t

Equal when,

40 + 10t = 12t

40 = 2t

t = 20 minutes

Each line will have:

12t = 12(20) = 240 barrels

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.

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step-by-step explanation:

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional