To determine how many minutes Shawna will spend solving 10 math problems at the same rate, we first need to calculate her rate from last night.
Last night, Shawna solved 15 math problems in 45 minutes. To find her rate (minutes per problem), we can divide the total time by the number of problems:
\[ \text{Rate} = \frac{45 \text{ minutes}}{15 \text{ problems}} = 3 \text{ minutes per problem} \]
Now, to find out how long it will take her to solve 10 math problems, we multiply the rate by the number of problems:
\[ \text{Time for 10 problems} = 10 \text{ problems} \times 3 \text{ minutes per problem} = 30 \text{ minutes} \]
Thus, Shawna will spend 30 minutes solving tonight's math problems.
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