Sam Loyd's Engineer's Puzzle - Solution
The Puzzle:
How long was the run between stations?
Our Solution:If the train takes x minute to cover 50 miles then its full-speed would be 50/x miles per hour and it's speed after blowing one of the cylinder would be 50/(x+40) miles per hour.
Therefore, (3/5) of (50/x)=50/(x+4x) gives X=60minutes or one hour; i.e. the full-speed of the train was 50 miles per hour and its three- fifth speed was 30miles per hour.
Suppose, the train needed to cover y miles when the cylinder blew. Then, {(y/50)+2} hour=y/30 hour gives y=150 miles. Since, the train already had covered 50 miles at full-speed before the cylinder blew, so the run between the stations was 50+150=200 miles.
Therefore, (3/5) of (50/x)=50/(x+4x) gives X=60minutes or one hour; i.e. the full-speed of the train was 50 miles per hour and its three- fifth speed was 30miles per hour.
Suppose, the train needed to cover y miles when the cylinder blew. Then, {(y/50)+2} hour=y/30 hour gives y=150 miles. Since, the train already had covered 50 miles at full-speed before the cylinder blew, so the run between the stations was 50+150=200 miles.
Puzzle Author: Loyd, Sam