Question

An eastbound train and a westbound train meet each other on parallel tracks heading in opposite directions. The eastbound train travels 14 miles per hour faster than the westbound train. After 2 hours, they are 272 miles apart. At what speeds are the two trains traveling?The east bound train is traveling ___ mph.The west bound train is traveling ___ mph.

Answer 1

Let e be the speed of the eastbound train, and w be the speed of the westbound train. Since the eastbound train travels 14 miles per hour faster than the westbound train, we'll have that

`e=w+14`

If after 2 hours the trains are 272 miles apart, we can say that:

`2e+2w=272`

Thereby, we'll have the following system of equations:

`\begin{cases}e=w+14 \\ 2e+2w=272\end{cases}`

Since we already have e in terms of w, let's go ahead and plug it in the second equation, and solve for w :

`\begin{gathered} 2e+2w=272 \\ \rightarrow2(w+14)+2w=272 \\ \rightarrow2w+28+2w=272 \\ \rightarrow4w=244\rightarrow w=(244)/(4) \\ \\ \Rightarrow w=61 \end{gathered}`

Now we've found w, let's plug in its value in equation 1 to find e :

`\begin{gathered} e=w+14 \\ \rightarrow e=61+14 \\ \Rightarrow e=75 \end{gathered}`

Therefore, we can conclude that the eastbound train is traveling at 75 mph, and the westbound train is traveling at 61 mph