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THE FARMER PROBLEM

QSF 131 JUNE 2009 FINAL PAPER

QUESTION 7 (8 marks)

Two neighbouring rural farmers, where one is considerably richer than the other, have to transport their produce on a daily basis to a town, 30 km further. The poor farmer, who only owns the most basic cart-and-horse transport, needs 1.5 kg of feed every hour for his horse, which costs R3.50 per 500 gram. The other farmer is fortunate to be able to use his 4×4 double cab which uses 15 litres of diesel every 100 km when he travels at an average  speed of 100 km/hr on the open road, and 20 litres of diesel per 100 km  when he has to travel at 60 km per hour.

The rich farmer travels at an average speed of 100 km per hour for 80% of the distance to the town, whereas for the remainder, he averages a speed of 60 km per hour. The poor farmer completes the 30 km journey in 3 hours. Calculate for the daily return journey:

(a)    the fuel costs to the rich farmer, if diesel costs R7.85 a litre;                               (5)

(b)   the difference between costs for the rich and the poor farmer.                          (3)

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