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Machines A and B always operate independently and at their respective constant rates. When working alone, Machine A can fill a production lot in 5 hours, and Machine B can fill the same lot in x hours. When the two machines operate simultaneously to fill the production lot, it takes them 2 hours to complete the job. What is the value of x ?

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Answer:

The value of x is
(10)/(3) hours.

Explanation:

Machine A = 5 hours

Machine B = x hours

Machine A and B = 2 hours

Using the formula:
(T)/(A)  + (T)/(B) = 1

where:

T is the time spend by both machine

A is the time spend by machine A

B is the time spend by machine B


(2)/(5)  + (2)/(x)  = 1

Let multiply the entire problem by the common denominator (5B)


5x((2)/(5)  + (2)/(x) = 1)

2x + 10 = 5x

Collect the like terms

10 = 5x - 2x

10 = 3x

3x = 10

Divide both side by the coefficient of x (3)


(3x)/(3)  = (10)/(3)


x = (10)/(3) hours.

Therefore, Machine B will fill the same lot in
(10)/(3) hours.

User Kshitij Dhakal
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