Word problem involving two trains traveling at different speeds, asking for the time it takes for the diesel train to catch up to the freight train.

A handwritten math problem on lined paper about two trains traveling at different speeds, with equations written below.

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Show Answer Key & Explanations Step-by-step solution for: Distance Word Problems

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- Let `x` be the number of hours the freight train traveled before being caught.
- The diesel train left 1 hour later, so it traveled for `x - 1` hours.
- Distance = Rate × Time.
- When the diesel train catches up, both trains have traveled the same distance.
- Freight train distance: `28 * x`
- Diesel train distance: `33 * (x - 1)`
- Set distances equal: `28x = 33(x - 1)`
- Expand the right side: `28x = 33x - 33`
- Subtract `28x` from both sides: `0 = 5x - 33`
- Add `33` to both sides: `33 = 5x`
- Divide by `5`: `x = 33/5`
- Simplify: `x = 6.6`

The freight train traveled for 6.6 hours before the diesel train caught up.

Parent Tip: Review the logic above to help your child master the concept of distance rate time word problems worksheet.

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