It takes 10 minutes for the two lines to have filled an equal number of barrels
Each line will have filled 90 barrels
<em><u>Solution:</u></em>
Let "x" be the number of minutes
<em><u>The old conveyer line has filled 20 barrels of paint, and is filling more at a rate of 7 barrels per minute</u></em>
Thus, a equation is framed as follows:
Old conveyor: 20 + 7(number of minutes)
Old conveyor: 20 + 7x ------- eqn 1
<em><u>A worker just switched on a newer line that can fill 9 barrels per minute</u></em>
Thus, a equation is framed as follows:
New conveyor: 9(number of minutes)
New conveyor: 9x -------- eqn 2
<em><u>In a little while, the two lines will have filled an equal number of barrels.</u></em>
<em><u>Thus, eqn 1 must be equal to eqn 2</u></em>
Thus it takes 10 minutes for the two lines to have filled an equal number of barrels
<em><u>How many barrels will each line have filled? </u></em>
Substitute x = 10 in any one of equations
Substitute in eqn 2
9x = 9(10) = 90
Thus each line will have filled 90 barrels