what time between 3 and 4 O' clock is the angle between the minute hand and the hour hand of a clock 75° ?
Answers
Given : Time in clock between 3 and 4 O' clock
Angle between the minute hand and the hour hand of a clock 75°
To find : Time
Solution:
Minute Hands 360° in 60 minutes
Hence 6° in 1 Minute
Hour Hands 360° in 12 * 60 minutes ( 12 hrs)
Hence 0.5° in 1 Minute
or 1° in 2 minutes
at 3 , Hour hand was already at 90°
Minute Had at 0°
Case 1 : Minute Hand Moved 15 + x° and Hour Hand moved x°
Then Angle Between them would be 75°
(15 + x°)/6 = x°/(0.5)
=> 15 + x° = 12x°
=> x° = 15/11
Time = 2 * 15/11 minutes = 30/11 mins
Time is 3 hrs 2 mins 44 sec
Case 2 : Minute Hand Moved 165 + x° and Hour Hand moved x°
Then Angle Between them would be 75°
(165 + x°)/6 = x°/(0.5)
=> 165 + x° = 12x°
=> x° = 165/11
=> x° = 15
Time = 2 * 15 minutes = 30 mins
Time is 3 hrs 30 mins
Two Possible Times are 3 :30 and about 3 hrs 2 mins 44 sec
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Step-by-step explanation:
Minute Hands 360° in 60 minutes
Hence 6° in 1 Minute
Hour Hands 360° in 12 * 60 minutes (12 hrs)
Hence 0.5° in 1 Minute or 1° in 2 minutes
at 3, Hour hand was already at 90° Minute Had at 0°
Hour Hand moved x°
Case 1: Minute Hand Moved 15 + x° and Then Angle Between them would be 75°
(15 + x)/6 = x/(0.5)
=> 15 + x = 12x°
=> x = 15/11
Time = 2 * 15/11 minutes = 30/11 mins
Time is 3 hrs 2 mins 44 sec.
Case 2: Minute Hand Moved 165 + x° and
Hour Hand moved xº
Then Angle Between them would be 75°
(165 + x)/6 = x°/(0.5)
=> x = 165/11
=> x = 15
Time = 2 * 15 minutes = 30 mins
Time is 3 hrs 30 mins
=> 165 + x = 12x°
Two Possible Times are 3:30 and about 3 hrs 2 mins 44 sec.