Question

In a paint factory, an old conveyer line has filled 20 barrels of paint, and is filling more at a rate of 7 barrels per minute. A worker just switched on a newer line that can fill 9 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

It takes 10 minutes for the two lines to have filled an equal number of barrels

Each line will have filled 90 barrels

Solution:

Let "x" be the number of minutes

The old conveyer line has filled 20 barrels of paint, and is filling more at a rate of 7 barrels per minute

Thus, a equation is framed as follows:

Old conveyor: 20 + 7(number of minutes)

Old conveyor: 20 + 7x ------- eqn 1

A worker just switched on a newer line that can fill 9 barrels per minute

Thus, a equation is framed as follows:

New conveyor: 9(number of minutes)

New conveyor: 9x -------- eqn 2

In a little while, the two lines will have filled an equal number of barrels.

Thus, eqn 1 must be equal to eqn 2

$20 + 7x =9x\\\\9x - 7x = 20\\\\2x = 20\\\\x = 10$

Thus it takes 10 minutes for the two lines to have filled an equal number of barrels

How many barrels will each line have filled?

Substitute x = 10 in any one of equations

Substitute in eqn 2

9x = 9(10) = 90

Thus each line will have filled 90 barrels