A country baker sent off his boy with a message to the butcher in the next village, and at the same time the butcher sent his boy to the baker.
One ran faster than the other, and they were seen to pass at a spot
720 yards from the baker’s shop.
Each stopped ten minutes at his destination and then started on the return journey, when it was found that they passed each other at a spot 400 yards from the butcher’s.
How far apart are the two tradesmen’s shops?
Of course each boy went at a uniform pace throughout.
Source: Henry Dudeney’s Canterbury Puzzles.
D
baker kid: x
butcher kid: y
720/x=(D-720)/y
D/x+10+400/x=D/y+10+(D-400)/y
(D+400)/x=(2D-400)/y
720y=(D-720)x
(D+400)y=(2D-400)x
let r=x/y
720=(D-720)r
D+400=(2D-400)r
D+400=(2D-400)720/(D-720)
(D+400)(D-720)=720(2D-400)
D^2-320D-288000=1440D-288000
D^2-1760D=0
D(D-1760)=0
D=0 or D=1760
D=1760
thus they are 1760 yards apart
|
|
Posted by Daniel
on 2017-04-27 11:58:56 |
solution
