Two clocks are set right at 10 text{ am}. One | vedclass

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(A) The time elapsed from $10 	ext{ am}$ on the first day to $4 	ext{ pm}$ on the following day is $30 	ext{ hours}$.The first clock gains $20 	ex

Vedclass · Accepted Answer

$3:59 \frac{2521}{4321} 	ext{ pm}$

Vedclass · Answer

(A) The time elapsed from $10 	ext{ am}$ on the first day to $4 	ext{ pm}$ on the following day is $30 	ext{ hours}$.The first clock gains $20 	ext{ seconds}$ in $24 	ext{ hours}$.This means $24 	ext{ hours} + 20 	ext{ seconds}$ (or $24 	ext{ hours} + \frac{20}{3600} 	ext{ hours} = 24 + \frac{1}{180} = \frac{4321}{180} 	ext{ hours}$) on the first clock corresponds to $24 	ext{ hours}$ of true time.Therefore,$1 	ext{ hour}$ on the first clock corresponds to $\frac{24}{4321/180} = \frac{24 	imes 180}{4321} 	ext{ hours}$ of true time.For $30 	ext{ hours}$ on the first clock,the true time elapsed is $\frac{24 	imes 180 	imes 30}{4321} = \frac{129600}{4321} 	ext{ hours}$.$\frac{129600}{4321} 	ext{ hours} \approx 29.993 	ext{ hours} = 29 	ext{ hours} + 0.993 	imes 60 	ext{ minutes} = 29 	ext{ hours} + 59 \frac{2521}{4321} 	ext{ minutes}$.Starting from $10 	ext{ am}$,adding $29 	ext{ hours}$ and $59 \frac{2521}{4321} 	ext{ minutes}$ results in $3:59 \frac{2521}{4321} 	ext{ pm}$.

Two clocks are set right at $10 \text{ am}$. One gains $20 \text{ seconds}$ and the other loses $40 \text{ seconds}$ in $24 \text{ hours}$. What will be the true time when the first clock indicates $4 \text{ pm}$ on the following day?

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