Mary commutes to work. On light traffic days it takes her only 15 minutes. On moderate days it takes 25 minutes and on heavy traffic days, it takes her 60 minutes. Only about 10% of the days are heavy traffic and 20% of the days the traffic is light. On average, how long does it take her to get to work?

marydien Dec 2, 2019

#1**+3 **

**Mary commutes to work. **

**On light traffic days it takes her only \(15\) minutes. **

**On moderate days it takes \(25\) minutes and **

**on heavy traffic days, it takes her \(60\) minutes. **

**Only about \(10 \%\) of the days are heavy traffic and **

**\(20 \%\) of the days the traffic is light. **

**On average, how long does it take her to get to work?**

\(\begin{array}{|rcll|} \hline \mathbf{\text{average}} &=& \dfrac{15\text{min.} \times 20\% + 25\text{min.} \times (100\%-20\%-10\%) + 60\text{min.} \times 10\%} {20~\%+(100\%-20\%-10\%)+10~\%} \\\\ &=& \dfrac{15\text{min.} \times 20\% + 25\text{min.} \times 70\% + 60\text{min.} \times 10\%} {100\%} \\\\ &=& 15\text{min.} \times 20\% + 25\text{min.} \times 70\% + 60\text{min.} \times 10\% \\ &=& 3\text{min.} + 17.5\text{min.} + 6\text{min.} \\ &=& \mathbf{26.5\text{min.}} \\ \hline \end{array} \)

heureka Dec 2, 2019