Question

freight train and an express train leave towns 390 km apart, traveling toward one another. The freight train travels 30 km per hour slower than the express train. They pass one another 3 hours later. What are their speeds? I think the speed of the freight may be 100km/hr and express would be 130km/hr, using the velocity = distance/time equation, but I am not quite sure of the formula and expression, or the answer for that matter. So if you could please help me I would appreciate it.

Answer 1

Answer: the speed of the express train is 80 km/h.

the speed of the freight train is 50 km/h.

Step-by-step explanation:

Let x represent the speed of the express train.

The freight train travels 30 km per hour slower than the express train. This means that the speed of the freight train would be (x - 30) km/h.

freight train and an express train leave towns 390 km apart, traveling toward one another. If they pass one another 3 hours later, it means that both trains travelled a total distance of 390 km in 3 hour.

Distance = speed × time

Distance travelled by freight train in 3 hours is

3(x - 30)

Distance travelled by express train in 3 hours is

3x

Since the total distance is 390 km, then

3(x - 30) + 3x = 390

3x - 90 + 3x = 390

6x = 390 + 90

6x = 480

x = 480/6

x = 80

The speed of the freight train is

80 - 30 = 50

Answer 2

Answer:

Freight: 50 km/hr

Express: 80 km/hr

Step-by-step explanation:

Express speed: x

Freight speed: x - 30

They're moving towards each other, so their combined speed would be:

x + (x - 30) = 2x - 30

Speed = distance/time

2x - 30 = 390/3

2x - 30 = 130

2x = 160

x = 80 km/hr

x - 30 = 50 kn/hr