Exploration: Grass Consumption by Oxen

If 6 acres of grass, together with what grows on the 6 acres during the time of grazing, keep 16 oxen for 12 weeks, and 9 acres keep 26 oxen 9 weeks, how many oxen will 15 acres keep 10 weeks, the grass growing uniformly all the time?*


*Problem taken from

Jones, S. I. (1930) Mathematical Wrinkles. Norwood, MA: Norwood Press. Problem 20, p. 3.


Here is a similar problem from Polya**. Polya attributes the problem to Newton.


If 12 Oxen eat up 3 1/3 acres of pasture in 4 weeks, and 21 oxen eat up 10 acres of like pasture in 9 weeks; to find how many oxen will eat up 24 acres in 18 weeks.


Polya, G. Mathematical Discovery: On understanding, learning, and teaching problem solving. Volume 1. New York: John Wiley. Problem 2.27, p 48.


Polya's Hint

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