John noticed that the angle formed by the minute hand and hour hand on a standard 12-hour clock was 110 degrees when he left home after 6 p.M.; it was also 110 degrees when he returned before 7 p.M. That same night. If he left home for more than five minutes, for how many minutes was he away?
Answers
Answer:
He was away from home for 63 minutes
Step-by-step explanation:
As he leaves home after 6 p.m. and at that time clock is making 110° angle i.e. when he leaves the home the must be 6hrs:13min:40sec, because on Exact 6 p.m. clock makes 180° angle, after that minute will move 10 min. i.e. 60° the angle reduces to 120°, now the time is 6:12, now 1 more it Moves i.e. 6° now the time is 6:13, now for 4° remaining it will move 40sec. so the final time when he leaves is 6hrs:13min:40sec.
Now after 7 when he returns home, the clock will make angle 110° at 7hrs:16min:40sec as the clock makes 180° angle at 7:05, After 10 min. at 7:15 it must be making an angle of 120°, after 1 more min. i.e. at 7:16 it will Be making an angle of 114°, after 40 sec. it will make an angle of 110°
Therefore when he returns home the time must be 7hrs:16min:40sec