A train leaves Union Station for Central Station, 216 km away, at 9 A.M. One hour later, a train leaves Central Station for Union Station. They meet at noon. If the second train had started at 9 A.M., and the first train at 10:30 A.M., they would still have met at noon. Find the speed of each train.

Let c be the speed of the train leaving Central

Let u be the speed of the train leaving Union

The total distance in either case is 216 km.

3u + 2c = 216
1.5c + 3u = 216

Solve these and you get
c=54
u=36

To find the speed of each train, we can use the formula: speed = distance/time.

Let's assume the first train's speed is x km/h and the second train's speed is y km/h.

We know that the first train leaves Union Station at 9 A.M. and meets the second train at noon, which is 3 hours later. So, the first train's travel time is 3 hours.

Using the formula, the distance traveled by the first train is given by: distance = speed * time.
For the first train: 216 km = x km/h * 3 hours.

Similarly, the second train leaves Central Station one hour later, which means it has a travel time of 2 hours (since they both meet at noon). So, the distance traveled by the second train is given by: distance = speed * time.
For the second train: 216 km = y km/h * 2 hours.

Now, let's consider the scenario where the second train leaves at 9 A.M. and the first train leaves at 10:30 A.M. In this case, the second train's travel time is 2.5 hours (since they still meet at noon).

Using the same formula as before, the distance traveled by the second train is given by: distance = speed * time.
For the second train: 216 km = y km/h * 2.5 hours.

From the given information, the distance traveled by both the first and second trains is the same (216 km).

Now, we can set up a system of equations to solve for the speeds of both trains:

Equation 1: 216 km = x km/h * 3 hours (when the first train leaves at 9 A.M.)
Equation 2: 216 km = y km/h * 2 hours (when the second train leaves at 9 A.M.)
Equation 3: 216 km = y km/h * 2.5 hours (when the first train leaves at 10:30 A.M.)

Using these equations, we can solve for x and y.

Equation 1 gives us: x = 216 km / 3 hours = 72 km/h.
Equation 2 gives us: y = 216 km / 2 hours = 108 km/h.
Equation 3 gives us: y = 216 km / 2.5 hours = 86.4 km/h.

Therefore, the speed of the first train is 72 km/h and the speed of the second train is 108 km/h.