Musa worked

Musa worked for 44 hours during one five days a week. His hours are from Monday through Thursday: 3 3/4, 6 7/12, 11 5/16, and 6 5/6.
Calculate the number of hours he worked on Friday.

Correct answer:

e =  15 ²⁵⁄₄₈ = 745/48 h

Step-by-step explanation:

$$\begin{gathered} a=3\frac{3}{4}=3+\frac{3}{4}=\frac{3\cdot 4+3}{4}=\frac{12+3}{4}=\frac{15}{4}=3.75\text{h} \\ b=6\frac{7}{12}=6+\frac{7}{12}=\frac{6\cdot 12+7}{12}=\frac{72+7}{12}=\frac{79}{12}\doteq 6.5833\text{h} \\ c=11\frac{5}{16}=11+\frac{5}{16}=\frac{11\cdot 16+5}{16}=\frac{176+5}{16}=\frac{181}{16}=11.3125\text{h} \\ d=6\frac{5}{6}=6+\frac{5}{6}=\frac{6\cdot 6+5}{6}=\frac{36+5}{6}=\frac{41}{6}\doteq 6.8333\text{h} \\ s=a+b+c+d=\frac{15}{4}+\frac{79}{12}+\frac{181}{16}+\frac{41}{6}=\frac{180}{48}+\frac{316}{48}+\frac{543}{48}+\frac{328}{48}=\frac{180+316+543+328}{48}=\frac{1367}{48}\doteq 28.4792\text{h} \\ w=44\text{h} \\ e=w-s=44-\frac{1367}{48}=\frac{44\cdot 48}{48}-\frac{1367}{48}=\frac{2112}{48}-\frac{1367}{48}=\frac{2112-1367}{48}=\frac{745}{48}=\frac{745}{48}\text{h}=15\frac{25}{48}\text{h}=15.5208\text{h} \end{gathered}$$

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