At what time between 5 and 6 o’clock are the hands of a clock 3 minutes apart?
Answer
Answer (as printed):
Explanation
At 5 o'clock, the minute hand is 25 min. spaces behind the hour hand. Case I. Minute hand is 3 min. spaces behind the hour hand. In this case, the minute hand has to gain $(25-3)=22$ minute spaces. 55 min. are gained in 60 min. 22 min. are gained in $\left(\frac{60}{55} \times 22\right) \mathrm{min} .=24 \mathrm{min}$. $\therefore$ The hands will be 3 min. apart at 24 min. past 5. Case II. Minute hand is 3 min. spaces ahead of the hour hand. In this case, the minute hand has to gain $(25+3)=28$ minute spaces. 55 min. are gained in 60 min. 28 min. are gained in $\left(\frac{60}{55} \times 28\right)=31 \frac{5}{11} \mathrm{min}$. $\therefore$ The hands will be 3 min. apart at $31 \frac{5}{11} \mathrm{min}$. past 5.