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

Answer:

The value of x is $\frac{10}{3}$ hours.

Step-by-step explanation:

Machine A = 5 hours

Machine B = x hours

Machine A and B = 2 hours

Using the formula: $\frac{T}{A} + \frac{T}{B} = 1$

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

$\frac{2}{5} + \frac{2}{x} = 1$

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

$5x(\frac{2}{5} + \frac{2}{x} = 1)$

2x + 10 = 5x

Collect the like terms

10 = 5x - 2x

10 = 3x

3x = 10

Divide both side by the coefficient of x (3)

$\frac{3x}{3} = \frac{10}{3}$

$x = \frac{10}{3}$ hours.

Therefore, Machine B will fill the same lot in $\frac{10}{3}$ hours.