Enigma 1726

Spoiler for New Scientist Enigma 1726: “Conspicuous consumption” (Follow the link to see the puzzle.)

Very straightforward. There are four unknown quantities: d1 and d2, the distances to your home and back, and g1 and g2, the gas used on the trip to your home and back. On the first visit he’s driven once to your home; second visit, twice to your home and once back; third visit, three times to your home and twice back. So

36.0 = d1/g1
42.5 = (2d1+d2)/(2g1+g2)
44.0 = (3d1+2d2)/(3g1+2g2)

and

71.5 = d1+d2+d3

Four linear equations in four unknowns. Solution: d1 = 13.5, d2 = 15.5, g1 = 0.375, and g2 = 0.25. Gas consumption on the way back was d2/g2 = 62 mpg. Must be downhill.

 

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