This doesn't make sense. You can say "let the number of days be a" but you cannot say then "a= U/V". You are told that U is a number of bags of feed and V is a number of horses. "U/V" has units of "bags of feed per horse".

No, it isn't. You are told that "X horses can eat through Y bags of feed in Z days." That means that Y/X is the "number of bags of feed per horse" for Z days, not one day.The rate of eating for each horse is Y/X per day

[/quote]V similar horses would consume V(Y/X) of bags per day[/quote]

Not "per day"- "per Z days".

For exactly the reason I said. Since "X horses can eat through Y bags of feed in Z days." "X/Y" would be the amount of feed per horse for Z days, not for one day. V(Y/X) is the amount of feed for V horses for Z days, not for one day. The amount of feed for V horses per day would be [V(Y/X)]/Z= (VY)/(XZ).Therefore it would take U/V(Y/X) days

Now my teacher corrected this by putting (UX/VY)Z which I do not understand. Could someone explain this very clearly? With many thanks...