Problem: A Manufacturing company uses two machines A and B with different production capacities. When working alone, machine A can produce a production lot in 5 hours and machine B can produce the same lot in x hours. When the two machines operate simultaneously to fill the same production lot, it takes them 2 hours to complete the job. How many hours will the machine B take to produce the production lot alone?

Correct Answer: $3\frac{1}{3}$ hours (Machine B)

Explanation:

Machine A takes 5 hours to produce = 1 lotMachine A takes 1 hours to produce = $\frac{1}{5}$ lotAnd machine B takes x hours to produce = 1 lotMachine B takes it hours to produce = $\frac{1}{x}$ lotTogether they take 1 hour to produce = $\frac{1}{5}$ + $\frac{1}{x}$= $\frac{x+5}{5x}$ Portion of lotAgain, they take 2 hours to complete the jobThey take 1 hour to complete $\frac{1}{2}$ job

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

=> x = $3\frac{1}{3}$ hours