We'll use variables to represent the speeds of the eastbound and westbound trains.
x will represent the speed of the eastbound train.
y will represent the speed of the westbound train.
The eastbound train is 16 mph faster than the westbound train. An equation can be made from this:
[tex]x - y = 16[/tex]
Subtraction is used, because it represents the difference in distances between the two trains if they travel the same direction.
After 4 hours, the trains are 800 miles apart. An equation can be made from this:
[tex]4x + 4y = 800[/tex]
Addition is used, because the trains are heading in opposite directions, which means their distances from the starting point are added together.
Set the two equations up vertically:
[tex]x - y = 16[/tex]
[tex]4x + 4y = 800[/tex]
We will use elimination to solve for x.
Multiply the entire first equation by 4 so that the coefficients for y will be opposite numbers:
[tex](x - y = 16) \times 4 = 4x - 4y = 64[/tex]
[tex]4x - 4y = 64[/tex]
[tex]4x + 4y = 800[/tex]
Combine the two equations together to cancel out y:
[tex]8x = 864[/tex]
Divide both sides by 8 to get x by itself:
[tex]x = 108[/tex]
The speed of the eastbound train is 108 mph.
