At what time between 7 o'clock and 8 o'clock | vedclass

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(D) At $7$ o'clock,the minute hand is $35$ minute spaces away from the hour hand.For the hands to be in a straight line but not together,they must be

Vedclass · Accepted Answer

$5\frac{5}{11}$ minutes past $7$

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(D) At $7$ o'clock,the minute hand is $35$ minute spaces away from the hour hand.For the hands to be in a straight line but not together,they must be $30$ minute spaces apart.Since the minute hand is at the $35$-minute mark,it needs to be at the $5$-minute mark (opposite to $7$) to form a straight line.To reach the $5$-minute mark from the $35$-minute mark,the minute hand must cover a relative distance of $35 - 30 = 5$ minute spaces.The minute hand gains $55$ minute spaces over the hour hand in $60$ minutes.Therefore,to gain $5$ minute spaces,the time taken is $\left(\frac{60}{55} 	imes 5ight) = \frac{60}{11} = 5\frac{5}{11}$ minutes.Thus,the hands will be in a straight line at $5\frac{5}{11}$ minutes past $7$.

At what time between $7$ o'clock and $8$ o'clock will the hands of a clock be in the same straight line but,not together?

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