A train leaves Atlanta at 1:00 PM. A second train leaves the same city in the same direction at 5:00 PM. The second train travels 48 mph faster than the first. If the second train overtakes the first at 9:00 PM, what is the speed of each of the two trains?
To find the speed of each train, let's break down the information given.
Let's denote the speed of the first train as 'x' mph. Since the second train is traveling 48 mph faster than the first, its speed will be 'x + 48' mph.
Now, let's consider the time each train has been traveling. The first train departs at 1:00 PM and is overtaken by the second train at 9:00 PM, which means it has been traveling for 8 hours. The second train departs at 5:00 PM and also reaches the first train at 9:00 PM, so it has only been traveling for 4 hours.
Since distance = speed × time, we know that the distance traveled by both trains is the same when they meet. Therefore, we can set up the equation:
Distance traveled by the first train = Distance traveled by the second train
To find the total distance traveled by each train, we can multiply their respective speeds by the time they have been traveling:
First train distance = x mph * 8 hours
Second train distance = (x + 48) mph * 4 hours
Setting these two distances equal, we get:
x * 8 = (x + 48) * 4
Now, we can solve this equation to find the value of 'x' - the speed of the first train:
8x = 4(x + 48)
8x = 4x + 192
4x = 192
x = 48
So, the speed of the first train is 48 mph.
Now, we can substitute this value back into the equation we used to find the speed of the second train:
Speed of the second train = x + 48 mph = 48 + 48 mph = 96 mph
Therefore, the speed of the first train is 48 mph and the speed of the second train is 96 mph.