Machine A was able to finish copying a set of document in 36 minutes. Machine B was brought in to work together with machine A to finish copying the document in 20 minutes. How long would it take machine B to finish copying the document by itself
A's rate ---- 1/36
B's rate ----- 1/x
combined rate = 1/36 + 1/x
= (x+36)/(36x)
1/( (x+36)/(36x) ) = 20
36x/(x+36) = 20
36x = 20x + 720
16x = 720
x = 45
it would take 45 min for B alone
just add up the amount of work done by A and B in a minute. Together, they do 1/20 of the job:
1/36 + 1/x = 1/20
To find out how long it would take machine B to finish copying the document by itself, we need to use the concept of "work rate". Work rate is a measure of how much work is done in a certain amount of time.
Let's assume the amount of work required to copy the document is 1 (it's arbitrary, but it makes the calculations simpler).
From the given information, we know that machine A can complete the work in 36 minutes, so its work rate is 1/36 of the document per minute.
When machine B joins, the combined work rate of machines A and B is sufficient to complete the job in 20 minutes. Using the concept of work rate, we can set up the equation:
1/36 + 1/B = 1/20
In this equation, B represents the work rate of machine B (the amount of work it can do in one minute), and 1/20 represents the combined work rate of machines A and B.
To solve for B, we can multiply both sides of the equation by the least common denominator, which is 720 (36 * 20):
(720/36) + (720/B) = (720/20)
20 + (720/B) = 36
Next, subtract 20 from both sides:
720/B = 36 - 20
720/B = 16
To isolate B, we can multiply both sides by B:
720 = 16B
Finally, divide both sides by 16:
720/16 = B
B ≈ 45
Therefore, it would take machine B approximately 45 minutes to finish copying the document by itself.