A clock

Mother set a clock right at 6:00 AM. If it gains 3 1/2 minutes per hour, what time will it show at 6:00 PM on the same day? Show your solution.

Result

t = 6:42 PM

Step-by-step explanation:

$$\begin{gathered} s=3\frac{1}{2}=3+\frac{1}{2}=\frac{3\cdot 2+1}{2}=\frac{6+1}{2}=\frac{7}{2}=3.5\text{min} \\ h=s\to \text{h}=s:60\text{h}=3.5:60\text{h}=0.05833\text{h} \\ t=6+12\cdot h=6+12\cdot \frac{7}{120}=6.7=6:42\text{PM} \end{gathered}$$

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