Question

Makayla and Takira enjoy writing poetry. In 27 weeks, Makayla can write 5 poems. It takes Takira 66 weeks to write 12 poems. On average, how many poems does Makayla write in one week? On average, how many poems does Takira write in one week? Use unit rates to determine who writes poems more quickly.

Answer 1

Makayla writes, on average,
`\((5)/(27)\)` poems per week, and Takira writes, on average,
`\((12)/(66)\)` poems per week.

Step-by-step explanation:

Makayla's rate of writing poetry can be determined by dividing the total number of poems she writes (5) by the total number of weeks (27).

Therefore, Makayla writes
`\((5)/(27)\)` poems per week. On the other hand, Takira's rate of writing poetry is found by dividing the total number of poems she writes (12) by the total number of weeks (66). Thus, Takira writes
`\((12)/(66)\)` poems per week.

To compare their rates more easily, it's beneficial to simplify these fractions. For Makayla,
`\((5)/(27)\)` simplifies to
`\((5)/(27)\)`, and for Takira,
`\((12)/(66)\)` simplifies to
`\((2)/(11)\)`. Now, it's evident that Makayla writes poems at a rate of
`\((5)/(27)\)` per week, and Takira writes at a rate of
`\((2)/(11)\)` per week.

To determine who writes more quickly, we compare the two rates. Since
`\((5)/(27)\)` is greater than
`\((2)/(11)\)`, Makayla writes poetry more quickly than Takira.

Therefore, using unit rates allows us to make a direct and clear comparison of their writing speeds, revealing that Makayla is the more prolific poet in terms of poems written per week.