Question

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 ?

Answer 1

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.