Starting Somethin' (Tribal Mix)

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Let's say one cow can eat X pounds of grass per day. The field grows Y pounds of grass per day. At the start the field already has N pounds of grass standing. At the end, the field has zero pounds of grass remaining. So we set up the equations for the amount of grass for the two cases, adding growing grass and subtracting eaten grass:for 96 days:N + 96Y - 20x96 X =0For 30 cows eating for 60 days:N + 60Y - 30x60 X = 0Or N + 96Y - 1920X = 0 andN + 60Y - 1800X = 0Subtract the two equations and we get: 36Y - 120X = 0, or 36Y =120X or 3Y = 10XIn other words, in one day ten cows can eat as much as the field grows in three days.Now we substitute this back into either of the two starting equationsto find how much grass (N) was in the field at the start:>N + 60Y - 1800X = N + 60Y -540Y = 0And N = 480YNow we set up the equation for 70 cows eating and the field growing for T days, until the grass is gone:N + TY - 70 TX = 0, or 480Y + TY - 21TY = 0 480Y -20TY = 0thus T = 24.So the 70 cows finish off the field in 24 days. 59ce067264

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