Respuesta :
[tex]\begin{array}{ccll} completion&hours\\ \cline{1-2} \frac{2}{5}&\frac{3}{4}\\[1em] x&1 \end{array}\implies \cfrac{~~ \frac{2}{5}~~}{x}=\cfrac{~~ \frac{3}{4}~~}{1}\implies \cfrac{2}{5x}=\cfrac{3}{4} \\\\\\ 8=15x\implies \cfrac{8}{15}=x[/tex]
The fraction of the project that the student can complete per hour is 8/15
What is unit rate?
There is independent quantity, and a quantity which depends on it (dependent quantity). When independent quantity moves by a unit measurement (single unit increment), the increment in dependent quantity is called rate of increment of dependent quantity per unit increment in independent quantity.
For this case the problem is asking about the amount of project that can be completed per hour.
The independent quantity is the time spent by student on the project.
The dependent quantity here is the amount of the project completed by the student in the time spent.
Thus, we get the unit rate of amount of project completed per unit amount of time (unit time is one hour here) as:
[tex]R = \dfrac{\text{Amount of project completed}}{\text{Time taken}} = \dfrac{2/5}{3/4} = \dfrac{2}{5} \times \dfrac{4}{3} = \dfrac{8}{15} \: \rm project / hour[/tex]
We used the fact that:
[tex]\dfrac{a}{b} = a \times \dfrac{1}{b}\\\\and\\\dfrac{1}{a/b} = \dfrac{b}{a}[/tex]
Thus, that student can complete the considered project's 8/15 part per hour.
Learn more about fractions here:
https://brainly.com/question/12106245
