The problem visible in the image involves two trains traveling on parallel tracks, with one train leaving one hour earlier than the other. The passenger train travels 5 mph faster than the freight train, and the passenger train catches up to the freight train after 10 hours. The task is to determine the speed of both trains.

Let's define the variables:

• Let the speed of the freight train be $x$ mph.
• Then, the speed of the passenger train will be $x + 5$ mph (since it's 5 mph faster).

Step 1: Time and distance relationships

• The freight train travels for 11 hours (because it left 1 hour earlier).
• The passenger train travels for 10 hours.

The distance traveled by both trains when the passenger train catches up must be the same.

Step 2: Set up the equation for distance

Using the formula $\text{distance} = \text{speed} \times \text{time}$:

• Distance traveled by the freight train in 11 hours: $11x$
• Distance traveled by the passenger train in 10 hours: $10(x + 5)$

Since the distances are equal, we can set up the equation: $11x = 10(x + 5)$

Step 3: Solve the equation

Now, let's solve for $x$.

$11x = 10(x + 5)$ $11x = 10x + 50$ $11x - 10x = 50$ $x = 50$

Step 4: Interpret the result

• The speed of the freight train is $50$ mph.
• The speed of the passenger train is $50 + 5 = 55$ mph.

So, the freight train is traveling at 50 mph, and the passenger train is traveling at 55 mph.

Let me know if you need further clarifications or have any questions!

Here are 5 related questions for practice:

1. If the passenger train was 10 mph faster, how long would it take to catch up?
2. What if the freight train left 2 hours earlier, how would the speeds change?
3. How far did the passenger train travel in the 10 hours?
4. If both trains had the same speed, how long would it take for the passenger train to catch up?
5. How much time would it take for the passenger train to catch up if it was traveling 7 mph faster than the freight train?

Tip: Whenever dealing with time and distance problems, ensure that the distances are equated to find unknown variables effectively.