The speed of a passenger train is 10mph faster than the speed of a freight train. The passenger train travels 340 in the same time it takes the freight train to travel 290 miles. Find the speed of each train?

If the passenger train travels 50 miles further at a speed that is 10 mph faster, then the travel time of each train is (50 mi)/(10 mi/hr) = 5 hr.

The speed of the passenger train is (340 mi)/(5 hr) = 68 mi/hr.
The speed of the freight train is (290 mi)/(5 hr) = 58 mi/hr.    (= 68 mph - 10 mph)