math
posted by israel .
how do i solve this: a Train leaves Poughkeepsie to grand central station in NYC at an average speed of 40 mph. a half hour later an express train leaves poughkeepsie station to NYC at a speed of 50 mph. both trains arrive at NYC the same time. based on this info calculate the distance between poughkeepsie and NYC

let the distance be x miles
time for first train = x/40
time for second train = x/50
x/40  x/50 = 1/2
times 200
5x  4x = 100
x = 100
Distance is 100 miles
check: to go 100 miles at 40 mph takes 100/40 hrs = 2.5
to go 100 miles at 50 mph takes 100/50 = 2hrs.
Does it take 1/2 less ? YES