Running at their respective constant rates, Machine X takes

[tim]

If you want to do even better, you can start by adding 2 days to 48/5 for x and subtracting 2 days from 48/5 for y, giving us 7.6 for y and 11.6 for x. However, subtracting the same amount from one time that you add to the other will actually speed up the process (consider how much time it takes if x and y both take 2 days to do a job versus 3 days for x and 1 day for y), so you have to slow the process down, forcing x to be larger than 11.6. Now you have backed into the correct answer since only one answer choice is larger than 11.6.

^^
... impressive.

if you could actually come up with this on the spot, in less time than it would take to just solve the problem, then ... well, even more impressive.

LOL yeah. I hope I've thoroughly managed to convey why estimation is NOT the way you want to do this one.

[RonPurewal]

well, if that stuff actually comes to mind quickly, it could be a viable way to do the problem. all i'm saying is that it's unlikely that that stuff will actually come to mind quickly.

the point is that, if you have a viable method in mind, JUST TRY IT. if you happen to pick a dead-end approach then you'll hit the wall quite soon, leaving you ample time to try other things.

[NinaP494]

If it takes 3 days to produce 5/4 widgets, it will take 3*(4/5) = 12/5 days to produce 1 widget.

If two machines were working at the same rate it would take, 2*12/5 i.e. approx 5 daysdays for x to produce 1 widget. Since machine X is slower it will take more than 5 days to produce 1 widget and subsequently more than 10 days to produce 2 widgets. The only answer more than 10 is 12 days. Answer E

[RonPurewal]

do you have a question? thanks.