Question Number 134145 by EDWIN88 last updated on 28/Feb/21
Commented by Ñï= last updated on 28/Feb/21
$${Any}\:{time}\:{any}\:\mathrm{2}\:{hands}\:{no}\:{coincide}.{I}\:{remember}. \\ $$
Commented by mr W last updated on 28/Feb/21
$${please}\:{explain}\:{what}\:{you}\:{mean}\:{sir}! \\ $$
Answered by mr W last updated on 28/Feb/21
$${assumed}\:{the}\:{hands}\:{move}\:{uniformly}. \\ $$$${say}\:{x}\:{minutes}\:{past}\:\mathrm{2}. \\ $$$${position}\:{of}\:{hour}\:{hand}:\:\mathrm{10}+\frac{{x}}{\mathrm{60}}×\mathrm{5} \\ $$$${position}\:{of}\:{minute}\:{hand}:\:{x} \\ $$$$\mathrm{10}+\frac{{x}}{\mathrm{60}}×\mathrm{5}={x} \\ $$$${x}=\frac{\mathrm{120}}{\mathrm{11}}=\mathrm{10}\frac{\mathrm{10}}{\mathrm{11}} \\ $$$$\Rightarrow\left({a}\right) \\ $$
Commented by mr W last updated on 28/Feb/21
$${old}\:{style}\:{clocks}\:{have}\:{hands}\:{which} \\ $$$${don}'{t}\:{move}\:{uniformly},\:{but}\:{stepwise}, \\ $$$${see}\:{Q}\mathrm{17449} \\ $$
Commented by EDWIN88 last updated on 28/Feb/21
$$\mathrm{yes}..\mathrm{thanks} \\ $$
Answered by bobhans last updated on 28/Feb/21
$$\therefore\mathrm{The}\:\mathrm{time}\:\mathrm{when}\:\mathrm{hands}\:\mathrm{be}\:\mathrm{together} \\ $$$$=\:\left(\mathrm{5}×\mathrm{n}×\frac{\mathrm{60}}{\mathrm{55}}\right)\:\mathrm{mins}\:\mathrm{past}\:\mathrm{n}\:\mathrm{o}'\mathrm{clock} \\ $$$$\mathrm{Here}\:\mathrm{n}=\mathrm{2} \\ $$$$=\:\mathrm{5}×\mathrm{2}×\frac{\mathrm{60}}{\mathrm{55}}\:=\:\frac{\mathrm{120}}{\mathrm{11}}\:=\:\mathrm{10}\:\frac{\mathrm{10}}{\mathrm{11}}\:\mathrm{mins}\:\mathrm{past}\:\mathrm{2} \\ $$
Commented by EDWIN88 last updated on 28/Feb/21
$$\mathrm{thanks} \\ $$