Answer:
20 minutes.
Explanation:
We have been given that the drain in your 45-gallon bathtub is partially clogged a partially clogged, but you need to take a shower. The shower head had a flow rate of 2.25 gallons per minute.
We will use rate formula to solve our given problem.
![\text{Work rate}=\frac{\text{Amount of work}}{\text{Time}}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/2nrust90d4n0e2oexrlj1u9m7yde8k924d.png)
![\text{Time}=\frac{\text{Amount of work}}{\text{Work rate}}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/758pfrvk9o7vvliyc7zgqe5d0a7kty893o.png)
![\text{Time}=\frac{45\text{ Gallons}}{\frac{\text{2.25 Gallons}}{\text{Minute}}}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/cwuqh9tirqokwmv2b10l31wdteh9sqy1le.png)
![\text{Time}=\frac{45\text{ Gallons}}{\text{2.25 Gallons}}* \text{Minute}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/m70v7sbt1c7ocmcrw5hqcf27vj7l75t8fe.png)
![\text{Time}=(45)/(2.25)* \text{Minute}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/nu8m5qrrb4qx2t9882vcwhl0emski48zea.png)
![\text{Time}=20 \text{ Minutes}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/24hgse11oix00ad22xi00oetjcsuhrjt4a.png)
Therefore, you can take a shower for 20 minutes at most.