another way: logical reasoning.
1. "machine X takes 2 days longer to produce w widgets than machine Y
" - machine X works slowly that machine Y
2. If machine Y work simultaneously, both machine would produce >4w widgets (Y faster than X)
3. So, 5w/4 in 3 days and >4w in ----> >9.6 days
4. in ~10 day Y can produce ~ 4w*2/(10-2) ~ w more widgets than X
5. therefore, answer has to be close to 3*(4w+w)/ (5w/4) = 12
It took ~30sec in my mind and is one of fast ways for solving work problems along with back-solving.
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