Math problem involving a freight train and a diesel train traveling east at different speeds, asking for the time it takes for the diesel train to catch up.

Let’s solve this step by step.

We are told:

- A freight train leaves San Diego going east at 28 mph.
- One hour later, a diesel train leaves the same place, same direction, at 33 mph.
- We need to find: How many hours did the freight train travel before the diesel train caught up?

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Step 1: Define variables

Let’s let x = number of hours the freight train traveled until the diesel train caught up.

Since the diesel train left one hour later, it traveled for (x - 1) hours when it caught up.

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Step 2: Use distance = rate × time

When the diesel train catches up, both trains have traveled the same distance from San Diego.

So:

Distance by freight train = 28 × x
Distance by diesel train = 33 × (x - 1)

Set them equal:

> 28x = 33(x - 1)

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Step 3: Solve the equation

Expand the right side:

> 28x = 33x - 33

Subtract 28x from both sides:

> 0 = 5x - 33

Add 33 to both sides:

> 33 = 5x

Divide both sides by 5:

> x = 33/5 = 6.6

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Step 4: Check the answer

Freight train travels 6.6 hours at 28 mph → distance = 28 × 6.6 = 184.8 miles

Diesel train travels 6.6 - 1 = 5.6 hours at 33 mph → distance = 33 × 5.6 = 184.8 miles ✔

They match — so our answer is correct.

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Final Answer:
6.6