Algebra 1-Using Rational Equations?

Question

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The speed of a freight train is 14 km/hr slower than the speed of a passenger train. The freight train travels 330 km in the same time that it takes the passenger train to travel 400 km. Find the speed of each train.

Answer 1

Let's say that the speed of the passenger train is p. This makes the speed of the freight train (p - 14), since the freight train is slower.

The distance that the passenger travels is given as 400 km. So, using the distance formula, d = rt, we see that 400 = pt, and we can solve for t: t = 400/p.

The distance for the freight train is also given, and we can write another formula: 330 = (p - 14)t. Solving for t, we have t = 330/(p - 14).

Since the question says that the distances are achieved in the same amount of time, we can set these two equations equal to each other:

400/p = 330/(p - 14)
400(p - 14) = 330p
400p - 4200 = 330p
70p = 4200
p = 60 km/h

So here, we see that the passenger train goes 60 km/h, and the freight train goes 44 km/h.