A train leaves a station and travels north at 75 km/h .Two hours later a second train leaves on a parallel...?

A train leaves a station and travels north at 75 km/h .Two hours later a second train leaves on a parallel track and travels north at 125 km/h .How far from the station will they meet?

Let t = 0 be the time when the first train leaves the station. That train's position a(k.e., distance from the station) s a function of time is given by:

x1(t) = t * 75 km/hr

The position of the second train as a function of time (still measuring time from when the first train left the station) is:

x2(t) = (t -2 hr)*125 km/hr (for t >=2)

When the trains meet, x1(t) = x2(t), so:

t * 75 km/hr = (t - 2 hr) * 125 km/hr

75*t = 125*t - 250 hr

250 hr = 50*t

5 hr = t

So the trains meet five hours after the first train leaves the station (three hours after the second train leaves the station).

In 5 hours the first train has traveled 5 hr * 75 kh/hr = 375 km, which should be the same distance as the second train travels in three hours (check -- 3 hr * 125 km/hr = 375 km!)

The trains meet 375 km from the station.