Sam Loyd's Engineer's Puzzle - Solution
The Puzzle:
Big Jim, engineer of the Oval Express says: "We blew off a cylinder head an hour after leaving the station and had to continue the trip at three-fifths of the former speed, which brought us in two hours late. If the accident had occurred fifty miles farther on, the train would have arrived forty minutes sooner".
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.
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.