Answer:
The value of x is [tex]\frac{10}{3}[/tex] hours.
Step-by-step explanation:
Machine A = 5 hours
Machine B = x hours
Machine A and B = 2 hours
Using the formula: [tex]\frac{T}{A} + \frac{T}{B} = 1[/tex]
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
[tex]\frac{2}{5} + \frac{2}{x} = 1[/tex]
Let multiply the entire problem by the common denominator (5B)
[tex]5x(\frac{2}{5} + \frac{2}{x} = 1)[/tex]
2x + 10 = 5x
Collect the like terms
10 = 5x - 2x
10 = 3x
3x = 10
Divide both side by the coefficient of x (3)
[tex]\frac{3x}{3} = \frac{10}{3}[/tex]
[tex]x = \frac{10}{3}[/tex] hours.
Therefore, Machine B will fill the same lot in [tex]\frac{10}{3}[/tex] hours.
