**Code:**

Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then machine Y, operating alone fore 3 hours, filled the rest of this lot. How many hours would it have taken machine X operating alone to fill the entire production lot if machine X produced twice as many bottles in 4 hours as machine Y produced in 3 hours?

I think this can be solved without setting up the equation.

We know this

machine X produced twice as many bottles in 4 hours as machine Y produced in 3 hours..............(1)

We also know that

machine X filled the production lot for 4 hours.

AND machine Y filled the production lot for 3 hours. .......................(2)

So from (1) and (2),

Machine X filled 2/3 of the production lot (IN its 4 hours)

To fill the whole lot.......it takes 4*3/2 = 6 hours