*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/g142.5 = (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.

Advertisements