Given the graphs of f(x) = -x + 2 and g(x) = 5x – 4, what is the solution to the equation f(x) = g(x)?
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Let be the speed of train A, and let's set the origin in the initial position of train A. The equations of motion are
where are the positions of trains A and B respectively, and t is the time in hours.
The two trains meet if and only if , and we know that this happens after two hours, i.e. at
Solving this equation for v we have
So, train A is travelling at 105 km/h. This implies that train B travels at