Question

two trains leave a station at the same time. one train is traveling north at a rate of 30 mph and the other train is traveling east at a rate of 40 mph. after 5 hours, how far apart are they in miles

Answer 1

After 5 hours, the northbound train is

(30 mph) (5 h) = 150 mi

north of the station, while the eastbound train is

(40 mph) (5 h) = 200 mi

east of the station.

The distance between the trains is the length of the hypotenuse in the right triangle formed by the trains' paths. By the Pythagorean theorem, this distance is

$\sqrt{(150\,\mathrm{mi})^2 + (200\,\mathrm{mi})^2} = \sqrt{62,500\,\mathrm{mi}^2} = \boxed{250\,\rm mi}$