Question

At what time between 3 and 4 is the minute hand 7 minutes ahead of the hour hand

Answer 1

Answer:

The minute hand is in between 3 and 4

The hour hand is 7 minutes back of minute hand

so the time is 2:17 or 2: 18

Answer 2

Answer: 3:24

Step-by-step explanation:

       12

        I

9 -----I----- 3

        I

       6

let's assume the indication above represents a clock.

The angle b/w 3 and 6 is 90°

∵ the angle between 3 and 4 is 90°/3 = 30°

we know,

Between 3 and 4 there are 5 mins / 5 units according to mins hand.

⇒ By the time the mins hand completes one rotation (i.e. 60 mins) hours hand moves from 3 to 4 (i.e. 5mins)

⇒ distance traveled by mins hand for 1 unit movement of the hour hand is  = total number of mins in one hour / no. of units traveled by hour hand in one hour

⇒ distance traveled by mins hand = 60mins / 5 = 12 mins

⇒ so, if the Hour hand moves 1 min or 1 unit then, the minute hand moves 12 mins / 12 units.

for next one minute travel of hour hand minute hand moves +12 mins

i.e. 24 mins in total.

here, hour hand will be passed 2 units from 3 and therefore, there will be 3 units remaining.

∴ by the time hour hand moves 2 units minute hand reaches to 24 mins.             .........(1)

Here, from (1)

hour hand is 3 mins away from 4 and

minutes hand is 4 mins away from 4

∴ total distance between betwwen hour hand and minute hand is 7 mins.

hence, the time then is 3:24

∴ the time between 3 and 4 is the minute hand 7 minutes ahead of the hour hand is 3:24

#SPJ2