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
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