How many times in a clock will the minute hand and the second hand overlap in 24 hours .?

Question

jacobbenvenutty · Answer

Just to help start off the problem they would overlap every 61 seconds. By the time the second hand went all the way around the clock a full minute (or 60 sec.) the minute hand would have already moved over by one dash on the clock face, adding an extra second travel time for the second hand to overlap the minute hand. (This is assuming they both started on the same position.)

mathmath333 · Answer

yes they start at same position

ganeshie8 · Answer

24*60 right ?

mathmath333 · Answer

No

mathmath333 · Answer

This question is same as two runners running in a circular track.
for 24 hrs.

ganeshie8 · Answer

do you mean they overlap only 24 times ?

mathmath333 · Answer

and how many times the fastest runner overtakes the slower till 24 hours. .

mathmath333 · Answer

no , how can they only overlap 24 times.

ganeshie8 · Answer

idk im just guessing... i think 24*60 looks good

ganeshie8 · Answer

in one hour seconds hand completes 60 revolutions and so there will be 60 overlaps right ?

mathmath333 · Answer

24*60 is the number of times the fastest runner(second hand) will complete the whole circle.

mathmath333 · Answer

in one hour seconds hand completes 60 revolutions and so there will be 60 overlaps if and only$\text{ if the minute hand is stationary}$.

anonymous · Answer

Try thinking about it this way.  Separate the two, the second hand will travel around the clock face "s" amount of times in a 24 hr period, and the minute hand will travel around "m" times in a 24 hr period.  so if you take (s-m)  and that is how many more times the second hand travels around overtaking the minute hand.

mathmath333 · Answer

$\large \begin{align} \color{black}{\normalsize \text{yes kclopp's answer this is correct}\hspace{.33em}\~\
\normalsize \text{it was simply to count and substract laps of full circle }\hspace{.33em}\~\
\normalsize \text{Number of overlaps}=\text{Number of laps of fast runner}\hspace{.33em}\~\
\normalsize-\text{Number of laps of slower runner}\hspace{.33em}\~\
\normalsize \text{Number of overlaps}=24\times 60-24\times 1 =1416\hspace{.33em}\~\
}\end{align}$

ganeshie8 · Answer

Nice!

mathmath333 · Answer

@jhonyy9

jhonyy9 · Answer

thank you very much @mathmath333