For what value of x does f(x) = g(x) when f(x) = 4x - 10 and g(x) = 0.5x + 7.5
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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:
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:
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:
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:
Combine the two equations together to cancel out y:
Divide both sides by 8 to get x by itself:
The speed of the eastbound train is 108 mph.
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:
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:
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:
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:
Combine the two equations together to cancel out y:
Divide both sides by 8 to get x by itself:
The speed of the eastbound train is 108 mph.