In five days, four black cows and three brown cows give as much milk, as five brown cows and three black cows would give in four days.

Which color cows are the best milk producers?

I will call the rate of bLack cow milk production L, in gallons of milk/cow/day. And I will call the rate of bRown cow milk production R in gallons of milk/cow/day.

(L*4 + R*3)*5 = (L*5 + R*3)*4
20L + 15R = 20L + 12R
15R = 12R
3R = 0

Does this mean that Brown cows produce no milk??? In that case, Black cows must be the best milk producers, though we don't know exactly how much they produce. Yes, L=0 is a solution, but then there wouldn’t be a best, and since the question wants to know which are the best I am assuming that the problem presupposes that there IS a best.

This is probably a trick and I probably fell for it, but this is my solution =)

Posted by nikki on 2004-09-03 10:55:18