Find the speed of each train if they are 270 miles apart 3 hours after the second train leaves chicago

Question

Two trains leave Chicago, Illinois, traveling in the same direction along parallel tracks.

The first train leaves 3 hours before the second, and its speed is 15 miles per hour faster than the second. Find the speed of each train if they are 270 miles apart 3 hours after the second train leaves Chicago.

Answer 1

60 and 75 mph

Let F = First train's speed

Let S = Second train's speed

The First train traveled for 6 hours

The Second train traveled for 3 hours

distance = speed times time traveled.

the First train traveled a distance of 6F

the Second traveled a distance of 3S

6F -3S = 270

6(S+15) -3S = 270

6S +90 -3S = 270

3S = 270-90 = 180

S = 180/3 = 60 mph

F = 60+15 = 75 mph