Respuesta :
Jhon was between 6:12 p.m and 6:52 p.m. So, Jhon left home for exact 40 minutes. Using the angle made by the hands in the clock, the required value is calculated.
How to find the angle between the minute hand and hour hand?
The general formula for finding the angle between the minute hand and the hour hand is
M = [tex]\frac{2}{11}[/tex] (H × 30 ± θ)
Calculation:
It is given that,
Jhon left home after 6 p.m with an angle of 110° formed by the minute hand and hour hand.
So,
M = [tex]\frac{2}{11}[/tex] (H × 30 - θ)
= [tex]\frac{2}{11}[/tex] (6 × 30 - 110)
= [tex]\frac{2}{11}[/tex] (180 - 110)
= [tex]\frac{2}{11}[/tex] × 70
= 140/11
So, he left after 6:12 p.m
Jhon returned home before 7 p.m with angle of 110° formed by the minute hand and hour hand.
M = [tex]\frac{2}{11}[/tex] (H × 30 + θ)
= [tex]\frac{2}{11}[/tex] (6 × 30 + 110)
= [tex]\frac{2}{11}[/tex] (180 + 110)
= [tex]\frac{2}{11}[/tex] × 290
= 580/11
So, he returned before 6:52 p.m
Then,
The time taken for returning home = 580/11 - 140/11 = 440/11 = 40 minutes.
Therefore, he took 40 minutes to return home.
Learn more about the angle made by hands in the clock here:
https://brainly.com/question/82007
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