A northbound train and a southbound train meet each other on parallel tracks heading in opposite directions. The northbound train travels 12 miles per hour faster than the southbound train. After 2.5 hours, they are 330 miles apart. At what speeds are the two trains traveling?

distance = speed * time

2.5(x+x+12) = 330
2x+12 = 132
2x=120
x=60

so, southbound speed is 60, northbound is 72

after 2.5 hours, the trains have traveled 150 and 180 miles, respectively.

A northbound train and a southbound train meet each other on parallel tracks heading in opposite directions. The northbound train travels 20 miles per hour faster than the southbound train. After 2.5 hours, they are 260 miles apart. At what speeds are the two trains traveling?

what is the equation using the information as it is given above that can be used to solve this problem ? using the variable
to represent the speed of the southbound train.

Let's assume the speed of the southbound train is "S" miles per hour.

According to the given information, the northbound train is traveling 12 miles per hour faster, so its speed would be "S + 12" miles per hour.

Now, we can calculate the distance traveled by each train after 2.5 hours.

Distance traveled by the southbound train:
Distance = Speed × Time
Distance = S × 2.5
Distance = 2.5S

Distance traveled by the northbound train:
Distance = Speed × Time
Distance = (S + 12) × 2.5
Distance = 2.5(S + 12)

According to the problem, their combined distance after 2.5 hours is 330 miles, so we can set up the following equation:

2.5S + 2.5(S + 12) = 330

Now, let's solve the equation:

2.5S + 2.5S + 30 = 330
5S + 30 = 330
5S = 330 - 30
5S = 300
S = 300 / 5
S = 60

Therefore, the speed of the southbound train is 60 miles per hour.

To find the speed of the northbound train, we can substitute the value of "S" into the expression (S + 12):

Speed of the northbound train = S + 12 = 60 + 12 = 72

Therefore, the speed of the northbound train is 72 miles per hour.

To solve this problem, we can set up a system of equations based on the given information. Let's denote the speed of the southbound train as 's' miles per hour.

Given that the northbound train travels 12 miles per hour faster than the southbound train, its speed can be represented as 's + 12' miles per hour.

Since the distance traveled by each train is equal to the speed multiplied by time, we can write the following equations:

Distance traveled by the southbound train = speed of the southbound train × time
Distance traveled by the northbound train = speed of the northbound train × time

After 2.5 hours, the distance between the trains is 330 miles. Therefore we can write the equation:

Distance traveled by the southbound train + Distance traveled by the northbound train = 330 miles

Using the equations mentioned above, let's set up the system of equations:

s × 2.5 + (s + 12) × 2.5 = 330

Now, we can solve this equation to find the value of 's', which represents the speed of the southbound train.

2.5s + 2.5(s + 12) = 330
2.5s + 2.5s + 30 = 330
5s + 30 = 330
5s = 300
s = 300/5
s = 60

Therefore, the speed of the southbound train is 60 miles per hour.

Since the northbound train travels 12 miles per hour faster, its speed would be 60 + 12 = 72 miles per hour.

Hence, the southbound train is traveling at a speed of 60 miles per hour and the northbound train is traveling at a speed of 72 miles per hour.