At what time between 4: 30 and 5 will the han | vedclass

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(C) At $4$ o'clock,the hands are $20$ minute spaces apart.For the hands to be in a straight line between $4:30$ and $5$,they must point in opposite di

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$54 \frac{6}{11}$ minutes past $4$

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(C) At $4$ o'clock,the hands are $20$ minute spaces apart.For the hands to be in a straight line between $4:30$ and $5$,they must point in opposite directions,meaning there is a space of $30$ minute spaces between them.Since the minute hand is behind the hour hand,it must gain $20 + 30 = 50$ minute spaces to be exactly opposite the hour hand.The minute hand gains $55$ minute spaces in $60$ minutes.Therefore,it gains $1$ minute space in $\frac{60}{55}$ minutes.To gain $50$ minute spaces,it takes $\frac{60}{55} 	imes 50 = \frac{12}{11} 	imes 50 = \frac{600}{11} = 54 \frac{6}{11}$ minutes.Thus,the required time is $54 \frac{6}{11}$ minutes past $4$.

At what time between $4: 30$ and $5$ will the hands of a clock be in a straight line?

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