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.

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27-10-2022
Mathematics

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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.

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CylahB312374 CylahB312374 · Answer 1 · 2022-10-27T14:46:23+02:00

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

[tex]e=w+14[/tex]

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

[tex]2e+2w=272[/tex]

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

[tex]\begin{cases}e=w+14 \\ 2e+2w=272\end{cases}[/tex]

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

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

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

[tex]\begin{gathered} e=w+14 \\ \rightarrow e=61+14 \\ \Rightarrow e=75 \end{gathered}[/tex]

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