Question

Running at their respective constant rates,
Machine A takes 4 days longer to produce x
widgets than Machine B. At these rates, if
the two machines work together to produce
2x widgets in 3 days, how many days would
it take Machine A alone to produce 5x/2
widgets?​

Answer 1

For work problems one of the most important thin to know is .

Let the time needed for machine X to produce widgets be days, so the rate of X would be ;

As "machine X takes 2 days longer to produce widgets than machines Y" then time needed for machine Y to produce widgets would be days, so the rate of Y would be ;

Combined rate of machines X and Y in 1 day would be (remember we can sum the rates). In 3 days two machines together produce 5w/4 widgets so: --> .

--> reduce by --> .

At this point we can either solve quadratic equation: --> --> or (which is not a valid solution as in this case , the time needed for machine Y to produce widgets will be negative value and it's not possible). So days is needed for machine X to produce widgets, hence time needed for machine X to produce widgets will be days.

OR try to substitute the values from the answer choices. Remember as we are asked to find the time needed for machine X alone to produce widgets then the answer should be among answer choices: E work - --> --> .

Answer: E.