Question

At what time between 4 and 5 o'clock are the hands of a clock together

Answer 1

Answer is 4 hrs and 240/11 min

i.e. 4hrs and 21.82 min or 4 hrs 21 min and 49 sec

We know minute hand of a clock covers 360 degrees in 60 min or 6 deg in 1 min and hour hand of a clock covers 360 deg in 12 hrs or 30 deg in i hour or .5 deg in 1 min.

So at 4:00 min hand has covered 0 degrees and hour hand has covered 120 degrees

Now let time after which these two coincide be x min.

So hour hand covers 120+x/2 upto that time and minute hand covers 6x degrees upto that time when they coincide the angles should be same

so 120+x/2 = 6x

solving we get x = 240/11 min

x=21.81mins

Answer 2

answer:

4 hrs and 240/11 min

i.e. 4hrs and 21.82 min or 4 hrs 21 min and 49 sec

Explanation:

we know minute hand of a clock covers 360 degrees in 60 min or 6 deg in 1 min

and hour hand of a clock covers 360 deg in 12 hrs or 30 deg in i hour or .5 deg in 1 min

so at 4:00 min hand has covered 0 degrees and hour hand has covered 120 degrees

now let time after which these two coincide be x min

so hour hand covers 120+x/2 upto that time

and minute hand covers 6x degrees upto that time

when they coincide the angles shud be same

so 120+x/2 = 6x

solving we get x = 240/11 min