Supppose two trains leave Holbrook, Arizona, at the same time, traveling in opposite directions. One train travels 10 mph faster than the other. In 3.5 hours, the trains are 322 miles apart. Find the speed of each train.

slow train --- x mph

faster train -- x+10

in 3.5 hrs,
slow train went 3.5x
fast train went 3.5(x+10)

solve for x:

3.5x + 3.5(x+10) = 322

42.42

41

train 1 = 41; train 2 = 51

To find the speed of each train, we can set up a system of equations based on the given information. Let's use the following variables:

Let s be the speed of the slower train in mph.
Then, the speed of the faster train will be s + 10 mph.

The distance traveled by the slower train in 3.5 hours is s * 3.5 miles.
The distance traveled by the faster train in 3.5 hours is (s + 10) * 3.5 miles.

Since they are traveling in opposite directions, the sum of their distances is equal to 322 miles.

Therefore, we can form the equation:

s * 3.5 + (s + 10) * 3.5 = 322

Now, we can solve this equation to find the speed of each train.

Step 1: Distribute the 3.5 on the left side of the equation:
3.5s + 3.5s + 35 = 322

Step 2: Combine like terms on the left side of the equation:
7s + 35 = 322

Step 3: Subtract 35 from both sides of the equation:
7s = 322 - 35
7s = 287

Step 4: Divide both sides of the equation by 7:
s = 287/7
s ≈ 41

So, the speed of the slower train is approximately 41 mph, and the speed of the faster train is 41 + 10 = 51 mph.