Train in minutes
A train travels 150 miles in 3 hours. At the same speed, how far does it travel in 90 minutes?
Asked: how far (miles). Is a: Find the missing value in a proportion. Answer: 75 miles.
| Phrase | Value | Counts | Needed? |
|---|---|---|---|
| “150 miles” | 150 miles | distance | yes |
| “3 hours” | 3 hours | time | yes |
| “90 minutes” | 90 minutes | new time | yes |
| Decision | Concept | Correct | Traps → wrong answer |
|---|---|---|---|
| What kind of question is this? | Recognize the question type | Same speed, new time: a missing value | — |
| Which two quantities go together? | Find the pair that forms the ratio | 150 miles in 3 hours | — |
| Are the two times in the same units? | Make units match | No: convert 90 minutes to hours | Use 90 as it is → 4500 |
| Which way round does the ratio go? | Keep the same order on both sides | Miles over hours on both sides | Hours over miles on one side → 0.03 |
The graph starts at the story. The Extract frame holds the decisions; red dashed arrows leave a decision for each trap and run to the wrong answer it produces. The thick green arrow carries the extracted numbers into the question, drawn exactly as on the question’s own page. Any follow-up step comes after, then the answer in the story’s terms. The legend is at the bottom.
| Trap | Mistake | Leads to | Caught by the answer? | Gives itself away with |
|---|---|---|---|---|
| Make units match | Uses 90 without converting minutes to hours. | 4500 | yes | 150 × 90 = 13500, 90 ÷ 3 = 30, 3 × 30 = 90 |
| Keep the same order on both sides | Flips one side: hours over miles. | 0.03 | yes | 3 × 1.5 = 4.5, 1.5 ÷ 150 = 0.01 |