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Two trains leave towns 1084 km apart at the same time and travel toward each other. One train travels 19 kmh faster than the other.
If they meet in 4 hours, what is the rate of each train?
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Solution 1. One equation.
Let x be the speed of the slower train, in km/h.
Then the speed of the faster train is (x+19).
The distance covered by the slower train in 4 hours is 4x.
The distance covered by the faster train in 4 hours is 4(x+19).
The equation is
4x + 4*(x+19) = 1084.
Simplify and solve for x.
Solution 2. Two equations
Let x be the speed of the slower train, in km/h, and
Let y be the speed of the faster train, in km/h.
Then you have this system of two linear equations
x + y = 
,
x - y = 19.
Simplify
x + y = 271,
x - y = 19.
Add the two equations.
From this point please complete the solution on your own.
