Answer:
[tex]\begin{array}{ccc}\text{Homework}&\text{Pepita}&\text{Francisco}\\ \\\text{Math}&\dfrac{1}{6}&\dfrac{1}{2}\\ \\\text{English}&\dfrac{2}{3}&\dfrac{1}{8}\\ \\\text{Science}&\dfrac{1}{6}&\dfrac{3}{8}\end{array}[/tex]
Step-by-step explanation:
Pepita and Francisco each spend a equal amount of time on homework. he table shows the fraction of time they spend on each subject.
[tex]\begin{array}{ccc}\text{Homework}&\text{Pepita}&\text{Francisco}\\ \\\text{Math}&&\dfrac{1}{2}\\ \\\text{English}&\dfrac{2}{3}&\\ \\\text{Science}&\dfrac{1}{6}&\dfrac{3}{8}\end{array}[/tex]
We know Pepita spent
[tex]\dfrac{2}{3}+\dfrac{1}{6}=\dfrac{2\cdot 2+1\cdot 1}{6}=\dfrac{5}{6}[/tex]
on English and Science.
Hence, Pepita spent
[tex]1-\dfrac{5}{6}=\dfrac{6}{6}-\dfrac{5}{6}=\dfrac{1}{6}[/tex]
on Math.
Francisco spent
[tex]\dfrac{1}{2}+\dfrac{3}{8}=\dfrac{1\cdot 4+3\cdot 1}{8}=\dfrac{7}{8}[/tex]
on Math and Science, so he spent
[tex]1-\dfrac{7}{8}=\dfrac{8}{8}-\dfrac{7}{8}=\dfrac{1}{8}[/tex]
on English.
The table is
[tex]\begin{array}{ccc}\text{Homework}&\text{Pepita}&\text{Francisco}\\ \\\text{Math}&\dfrac{1}{6}&\dfrac{1}{2}\\ \\\text{English}&\dfrac{2}{3}&\dfrac{1}{8}\\ \\\text{Science}&\dfrac{1}{6}&\dfrac{3}{8}\end{array}[/tex]
