Question

Two trains leave the city going opposite directions, one going north and the other going south. The northbound train is traveling 14 mph slower than the southbound train. After 3 hours the trains are 498 miles apart. Find the speed of each train

Answer 1

Let the speed of the southbound train be x mph. then the speed of the northbound train will be x - 14 mph.

Both trains are traveling in the opposite direction and going away from each other.

The distance traveled by southbound train in 3 hours will be 3x miles. The distance traveled by southbound train will be 3(x - 14) miles.

Therefore, the sum of distance covered by both the trains will be equal to 498 miles.

`\begin{gathered} 3x+3(x-14)=498 \\ 3x+3x-42=498 \\ 6x-42=498 \\ 6x-42+42=498+42 \\ 6x=540 \\ x=90 \end{gathered}`

Thus, the speed of the southbound train is 90 mph and the speed of the northbound train is 76 mph.