Question

A freight train leaves the train station 4hrs before a passenger train. The two trains are traveling in the same direction on parallel tracks. If the rate of the passenger train is 40 mph faster than the freight train, how fast is each train traveling if the passenger train passes the freight train in 6hrs?

Answer 1

The speed of the freight train is 60 mph, and the speed of the passenger train is 100 mph. This is determined by setting up equations representing the distance each train has traveled when the passenger train catches up and solving for the speed of the freight train.

Step-by-step explanation:

To solve the problem involving the two trains, we need to set up a system of equations based on the information given. We are told that the passenger train leaves 4 hours after the freight train and that it travels at a speed that is 40 mph faster. Furthermore, the passenger train catches up with the freight train in 6 hours. Let's denote the speed of the freight train as x mph and the speed of the passenger train as x + 40 mph.

Since the freight train has a 4-hour head start, it travels for a total of 10 hours by the time the passenger train catches up. The passenger train, on the other hand, travels for 6 hours. We can now set up the following equations based on the distances each train travels, which will be equal at the point of overtaking:

Distance traveled by freight train = speed of freight train × time of travel for freight train

Distance traveled by passenger train = speed of passenger train × time of travel for passenger train

By substituting the expressions for speed, we get:

(Freight train distance) x × 10

(Passenger train distance) (x + 40) × 6

As the distances are equal at the moment of overtaking, the equations can be set equal to each other:

x × 10 = (x + 40) × 6

Solving for x:

10x = 6x + 240

4x = 240

x = 60 mph (speed of freight train)

The passenger train's speed will be x + 40 mph = 100 mph.

Answer 2

It can be said that most of the required information's are already given in the question.
Let us assume the speed of the passenger train = x
Speed of the freight train = y
x = y + 40
The second equation will be
6 * x = 10 * y
6x = 10y
Dividing both sides by 2, we get
3x = 5y
x = 5y/3
Putting the value of "x" in the first equation, we get
x = y + 40
5y/3 = y + 40
5y = 3y + 120
5y - 3y = 120
2y = 120
y = 60 mph
Putting the value of y in the first equation, we get
x = y + 40
= 60 + 40
= 100 mph
From the above deduction, we can conclude that the passenger train is traveling at 100 mph and the freight train is traveling at 60 mph.