Classmate 2613

Juro didn't have a watch, so he asked a classmate for the exact time. Simon looked at the clock and said: "If my watch were 22 minutes late, it would be 11:54. But it's not that much because my watch doesn't miss; it goes 22 minutes ahead". What time was it when Juro asked?

Result

h = 12:38

Step-by-step explanation:

$$\begin{gathered} m=22\text{min}\to \text{h}=22:60\text{h}=0.36667\text{h} \\ {h}_1=11:54=11hr54min=11+\frac{54}{60}=11.9hr=11.9 \\ x-m=h_1 \\ x+m=h \\ (h_1+m)+m=h \\ (11.9+0.36666666666667)+0.36666666666667=h \\ h=12.633333=12.63333=12:38 \\ h=\frac{12.63333333}{1}=12.63333333 \\ h=\frac{379}{30}\doteq 12.633333 \\ x=h_1+m=11.9+0.3667=\frac{184}{15}=12\frac{4}{15}\doteq 12.2667\text{h} \end{gathered}$$

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