I need help with an Algebra word problem!

One conveyor belt can move 1000 boxes in 12 minutes. Another can move 1000 boxes in 6 minutes. If another conveyor belt is added and all three are used, the boxes are moved in 3 minutes. How long would it take the third conveyor belt alone to do the same job? (Round your answer to the nearest tenth, if necessary.)

Thanks!

Calculate the speed of the two first conveyor belts and let's say that the speed of the third conveyor belt is v3 (velocity 3).

v1 = 1000/12 = 250/3 boxes per minute
v2 = 1000/6 = 500/3 boxes per minute

Don't divide any further because numbers with endless decimals show up.

If another conveyor belt is added and all three are used, the 1000 boxes are moved in 3 minutes. This can be expressed this way:

v1*3 + v2*3 + v3*3 = 1000 ----->

(250/3)*3 + (500/3)*3 + v3*3 = 1000 ----->

250 + 500 + v3*3 = 1000 ----->

v3*3 = 250 -----> v3 = 250/3 boxes per minute

Notice that it was much tidier working with the fractions. Also notice that v3 equals v1 = 250/3 boxes per minute, and since it takes the first conveyor belt 12 minutes to do the job alone, this is the same for the third belt, so your answer is 12 minutes. Two other ways to see it:

v3 = 250/3 boxes per minute

Doing the job alone, v3*x = 1000 -----> x = 1000 / (250/3) ----->

x = 12 minutes

Or:

250/3 boxes ------------ 1 minute
1000 boxes ------------- x minutes

x = 1000*1/(250/3) -----> x = 12 minutes

I hope this helps...