There is a disk as shown in a figure and three needles which continue rotating with a fixed speed clockwise respectively around the center O of the disk.
The time concerning a needle rotating one time is 5 minutes, 8 minutes, and 14 minutes sequentially from a long needle.
All of three needles overlapped at a certain time.
Find the time concerning all of three needles overlapping next.
The time concerning a needle rotating one time is 5 minutes, 8 minutes, and 14 minutes sequentially from a long needle.
All of three needles overlapped at a certain time.
Find the time concerning all of three needles overlapping next.
Answer
Time to find is the time concerning two cycles between overlapping of A and B and overlapping of A and C come to be same.
The time cycle A and B overlaps is the time concerning A catching up with B and it is 360 /(72 - 45) = 40/3 minutes.
The time cycle A and C overlaps is the time concerning A catching up with C and it is 360 / (72 - 180/7) = 709 minutes.
The time concerning two cycle overlap should be found by calculating the least common multiple of 40/3 and 70/9.
The time to find is 850/9 minutes.
850/9 minutes
Solution
Three needles are set to A, B, and C from the longer one in order.
Time to find is the time concerning two cycles between overlapping of A and B and overlapping of A and C come to be same.
Find the angle which A, B, and C advances in one minute respectively.
A : 360 degree / 5 minutes = 72 degrees/minute
B : 360 degree / 8 minutes = 45 degrees/minute
C : 360 degree / 14 minutes = 180/7 degrees/minute
A : 360 degree / 5 minutes = 72 degrees/minute
B : 360 degree / 8 minutes = 45 degrees/minute
C : 360 degree / 14 minutes = 180/7 degrees/minute
The time cycle A and B overlaps is the time concerning A catching up with B and it is 360 /(72 - 45) = 40/3 minutes.
The time cycle A and C overlaps is the time concerning A catching up with C and it is 360 / (72 - 180/7) = 709 minutes.
The time concerning two cycle overlap should be found by calculating the least common multiple of 40/3 and 70/9.
The time to find is 850/9 minutes.
