Solve the problem and answer the question.
-One conveyor belt can move 1000 boxes in 11 minutes. Another can move 1000 boxes in 8 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?

Question

Quizplus · Accepted Answer

Let x be the time taken by the third conveyor belt alone to move 1000 boxes.
Then, the rate of the first conveyor belt is 1000/11 boxes per minute.
The rate of the second conveyor belt is 1000/8 boxes per minute.
The rate of the three conveyor belts combined is 1000/3 boxes per minute.
Using the formula rate x time = work, the total work done by the three conveyor belts is 3000 boxes.
Thus, we can write the equations:
(1000/11) * 3 + (1000/8) * 3 + (1000/x) * 3 = 3000
Simplifying this equation, we get:
x = 22/3 minutes or 7.33 minutes
Therefore, the third conveyor belt alone would take 7.33 minutes to move 1000 boxes. 
Choice B is correct because 7.33 is closest to answer choice 7.3. Let x be the rate of the third conveyor belt (in boxes/minute).
Working together, the three conveyor belts can move 1000 boxes in 3 minutes:

3(1000/11 + 1000/8 + 1000/x) = 1000

Multiplying both sides by (11)(8)(x) gives:

24x(240 + 330x + 88x) = 11(8)x(1000)

Simplifying, we get:

792x^2 + 825x - 2750 = 0

Factoring, we get:

(22x - 25)(36x + 110) = 0

Since x represents a rate, it must be positive. Therefore:

x = 25/22

So the third conveyor belt can move 1000 boxes in:

1000/(25/22) = 880 seconds = 14 minutes and 40 seconds.

Therefore, the correct answer is B.

Solve the Problem and Answer the Question