Two trains start from towns 224 mi apart and travel towards each other on parallel tracks. They pass each other 1.6 hr later. If one train travels 10 mph faster than the other, find the speed of each train.

65mph, 75mph

Explanation:

Let us assume x to be the speed of the slower train, in mph (miles per hour).

Then the speed of the other train is (x+10) mph, according to the question.

We then would have an equation like this

1.6x + 1.6(x+10) = 224.

This is because, the first addend in the left side is the distance covered by the slower train.

The second addend in the left side is the distance covered by the faster train.

The sum is 224 miles, because they together covered all the distance to the moment when they meet each other.

1.6x + 1.6x + 16 = 224

3.2x + 16 = 224

3.2x = 224 - 16

3 2x = 208

x = 208/3.2

x = 65

Thus the speed of the slower train is 65mph, and that of the other train is 65 + 10 = 75mph

where are the vectors ?