A computer printed 176400 lines in a given day. If the printer was in operation for 7 hours during the day, how many lines did it print per minute?

### Concept & Formula This is a basic rate problem. To find the rate per minute, you must divide the total work done by the total time taken in minutes. $$ \text{Rate} = \frac{\text{Total Lines}}{\text{Total Minutes}} $$ ### Step-by-Step Solution * **Given:** Total lines = 176400. Total time = 7 hours. * **Conversion:** First, convert hours into minutes. * Total minutes = $7 \times 60 = 420$ minutes. * **Calculation:** Divide the total lines by the total minutes. * Rate = $\frac{176400}{420}$ * Cancel out the zeros: $\frac{17640}{42}$ * Simplify by dividing by 7: $\frac{2520}{6}$ * Simplify by dividing by 6: $420$. ### Exam Strategy & Shortcut Look at the numbers: $1764$ is a multiple of $7$. $\frac{1764}{7} = 252$. Then you just need to divide by 60 (for minutes). $\frac{25200}{60} = 420$. Handling the hours division first keeps the numbers smaller. ### Common Pitfall Failing to convert hours to minutes. A student might do $\frac{176400}{7} = 25200$ and then get confused when it doesn't match the options, or worse, make a secondary math error trying to force an answer. Always align the units first. ### Final Answer **Therefore, the correct answer is 420.**