Final answer:
Patrick will take a total of 21/4 hours or 2.25 hours to complete his science project, as he completes 1/3 of the project in 3/4 of an hour.
Step-by-step explanation:
The question asks how many hours it will take for Patrick to complete his science project if he completes 1/3 of it in 3/4 of an hour. To find the time Patrick needs to complete the entire project, we need to determine how much time he takes to complete one whole project based on the fraction of the project he completed in 3/4 of an hour.
First, we'll consider the fraction of the project he has completed: 1/3 of the project. He does this in 3/4 of an hour. We can then set up the proportion like so:
(1/3 of project) / (3/4 of hour) = (1 whole project) / (x hours)
By cross-multiplying, we have:
1/3 * x = 3/4
x = (3/4) / (1/3)
x = (3/4) * (3/1)
x = 9/4 hours
When we calculate this, we get that x = 9/4, which simplifies to 21/4 hours or 2.25 hours. This means it will take Patrick 2 hours and 15 minutes to complete his entire science project.