# The Hour Hand And Minute Hand Of The Clock Exchanged Places

**Problem**

Between 3:00 and 4:00, Kathryn looked at her watch and noticed that the minute hand was between 5 and 6. Later, Kathryn looked again and noticed that the hour hand and the minute hand had exchanged places. What time was it in the second case?

**Solution**

**First look at the watch**

$x - \frac{1}{12}y = 25$ ← Equation (1)

**Second look at the watch**

$-\frac{1}{12}x + y = 15$ ← Equation (2)

**From Equations (1) and (2)**

$x = 26.43$

$y = 17.20$

Time in the 2^{nd} case = 5:17.20 ← *answer*

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