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kvasek [131]
3 years ago
15

Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 16 miles per hou

r faster than the westbound train. If the two trains are 800 miles apart after 4 hours, what is the rate of the eastbound train? Do not do any rounding.
Mathematics
1 answer:
Verizon [17]3 years ago
5 0
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:

x  - y = 16

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:

4x + 4y = 800

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:

x - y = 16
4x + 4y = 800

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:

(x - y = 16) \times 4 = 4x - 4y = 64

4x - 4y = 64
4x + 4y = 800

Combine the two equations together to cancel out y:

8x = 864

Divide both sides by 8 to get x by itself:

x = 108

The speed of the eastbound train is 108 mph.
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