A man on his way to dinner shortly after 6.00 p.m. observes that the hands of his watch form an angle of 1100. Returning before 7.00 p.m. he notices that again the hands of his watch form an angle of 1100. Find the number of minutes that he has been away.
Answers
Step-by-step explanation:
Since each minute make an angle of 6 degree to previous minute 110 degree is about 19 minutes. So back from 6 he leaves at 6: 11 pm.
Also, at 7 the time at which the angle is 110 is 7:21 pm
So he is out for 1 h 10 min i.e. 70 min
Answer:
Step-by-step explanation:
At 6 PM, the hand will form an angle of 180°
The minute hand makes a full rotation in 1 hour.
Thus, every minute, the minute hand moves = 1/60 rotation
= 360/60 = 6°
The hour hand makes a full rotation in 12 hours.
Every minute, the hour hand moves 1/(60 × 12)
= 360/720
= 1/2 or 0/5°
Dinner between 6:00 and 7:00 hour hand moves = 360°/12 hours
= 360°/(12*60)
= 0.5°/minute
The relative rate difference = 6° - 0.5°
= 5.5°/minute
The minute hand movement in respect to the hour hand was from -
= 110 (before dinner) + 110 (after dinner)
= 220
220° /5.5°
= 40
Thus, the number of minutes he has been away is 40.