Two trains depart at the same time from the same station and travel in opposite directions. One train travels 25 mph faster than the other train. After 2 hours the trains are 162 miles apart. Find the speed of each train.
If they travel in opposite directions, then just add their distances
distance = speed * time
2x + 2(x+25) = 162
4x + 50 = 162
4x = 112
x = 28
so, the slow train travels 28 mph
the fast train travels 53 mph
To find the speed of each train, let's assign variables to the unknowns. Let's call the speed of one train "x" mph. Since the other train is traveling 25 mph faster, we can call its speed "x + 25" mph.
Now, let's break down the information given in the problem. Both trains depart at the same time and travel in opposite directions. We know that the distance between the trains after 2 hours is 162 miles.
To solve this problem, we can use the formula Distance = Speed * Time. For the first train, the distance it travels in 2 hours is 2x miles. For the second train, the distance it travels in 2 hours is 2(x + 25) miles.
Since they are traveling in opposite directions, the sum of their distances should be equal to 162 miles:
2x + 2(x + 25) = 162
Simplifying this equation, we start by distributing the 2 on the second term:
2x + 2x + 50 = 162
Combining like terms:
4x + 50 = 162
Next, we can isolate the variable by subtracting 50 from both sides of the equation:
4x = 162 - 50
4x = 112
Finally, divide both sides of the equation by 4 to solve for x:
x = 112/4
x = 28
So, the speed of the first train is 28 mph.
To find the speed of the second train, which is 25 mph faster, we add 25 to the speed of the first train:
x + 25 = 28 + 25 = 53
Therefore, the speed of the second train is 53 mph.