A train leaves Orlando at 3:00 PM. A second train leaves the same city in the same direction at 5:00 PM. The second train travels 20 mph faster than the first. If the second train overtakes the first at 10:00 PM, what is the speed of each of the two trains?
To determine the speed of each train, we can first calculate the time it takes for the second train to catch up to the first train. Since the second train leaves 2 hours after the first train (at 5:00 PM) and catches up to it at 10:00 PM, the catching-up time is 5 hours.
Next, we'll define the speed of the first train as x mph. Since the second train travels 20 mph faster than the first train, its speed can be defined as (x + 20) mph.
Now, we can apply the formula d = rt, where d represents distance, r represents rate (or speed), and t represents time.
For the first train, the distance traveled is (x mph) * (5 hours). So, the distance traveled by the first train is 5x miles.
For the second train, the distance traveled is [(x + 20) mph] * (5 hours). So, the distance traveled by the second train is 5(x + 20) miles.
Since the second train catches up to the first train, the distances traveled by both trains are equal. Therefore, we can equate the two distances and solve for x:
5x = 5(x + 20)
Let's solve this equation:
5x = 5x + 100
-5x + 5x = 100 - 5x
0 = 100
This equation has no solution, which means there is an error in the problem statement.
Train A went for 2 hours before B started.
B, going 20 mph faster took 5 hours to catch up.
So A was 100 miles ahead.
That means A went 100 miles in 2 hours.
I think you can take it from here, no?