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I'd like to see your solutions to this one. And please explain your process.
Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce (5/4)w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?
LEt Y produce w widgets in a days
X shall produce w widgets in a+2 days
X in 1 days shall produce w/a+2 widgets
Y in 1 day shall produce w/a widgets
If 5/4 widgets are produced in 3 days, then in 1 days 5/12 widgets shall be produced
SO if X produces w/a+2 widgest and Y produces w/a widgets in one day, the combined they shall produce w/a+2 + w/a which is equal to 5/12
so setting up the equation
w/a+w/a+2 = 5/12
solving this equation, we get a=4 & -6/5. Since days cannot be in -ve, so ahas to be 4.
Now, if X produces w widgets in a+2=6 days, then it shall produce 2w widgets in 6*2=12 days.
so 12 days in the answer