Question

At what time between 3 and 4 is the minute hand 4 minutes behind the hour hand

Answer 1

given time is in between 3 and 4
so let hour hand on 3
and at 3:15 both hand will be on 3
we need minute hand 4 min behind the hour hand
3:15-0:04= 3:11
so at 3:11 the min hand will be 4 min behind the hour hand approximately
or
you can do it by the traditional formula
formula--angle=30H-11/2m
let the time is HH:MM 03:--
using the formula
angle travel by min hand =6°m
angle traveled by hour hand =30*6-11/2=( 180-m)*0.5
90+0.5m°
given difference 4 min
4*6=24°
90-0.5-6m=24
5.5m=66
m=66/5.5=12
so time will be 3:12

Answer 2

Question effectively asking for the time between 3 and 4 o' clock when the angle between the two hands is 24°.

Let the time be 3:m

Angle travelled by minute hand = 6m°

Angle travelled by hour hand = (180 + m)x0.5°

= 90 + 0.5m°

Given, difference between the two is 24°.

90 + 0.5m - 6m = 24

=> 5.5m = 66

m = 66/5.5 = 12

=> The time is 3:12 am or 3:12 pm

hope it helps u