How Many Oxen Can Be Fed?From: Anonymous Date: Fri, 28 Jun 1996 9:22:58 -0400 (EDT) Subject: three pastures I don't understand this problem. Can you help me? We have three pastures with grass of identical height, density, and growth rate. The first is three and one-third acres and can feed 12 oxen for 4 weeks. The second is 10 acres and can feed 21 oxen for 9 weeks. The third is 24 acres. How many oxen can be fed on it for 18 weeks? Date: Fri, 28 Jun 1996 13:33:35 -0400 (EDT) From: Dr. Anthony Subject: three pastures We must take account of growth of pasture while the cattle are feeding. Let e = extra growth per acre per week. So in the first situation: Total pasture = 3.5(1 + 4e) = k*12*4 (k=constant of proportionality) In the second situation we have Total pasture = 10(1 + 9e) = k*21*9 Dividing these expressions to eliminate k we get: 3.5(1+4e)/{10(1+9e)} = 48/189 3.5(1+4e) = 2.54(1+9e) 1+4e = 0.725623(1+9e) 1+4e = 0.725623 + 6.5306e 0.274377 = 2.5306e and so e = 0.1084237 and k = 10(1+9e)/189 = 0.10454 Then in the last situation if x = number of oxen we have: 0.10454*18x = 24(1+18e) = 24(1+18*0.1084237) = 70.839 x = 70.839/(0.10454*18) = 37.645 oxen - say 37 oxen We could feed 37 oxen for 18 weeks on 24 acres. -Doctor Anthony, The Math Forum |
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