SOLUTION: Three lighthouses on three nearby islands flash their lighys every evening. On one island, the light flashes every 45 seconds. The lighthouse on the second island has a light that

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Three lighthouses on three nearby islands flash their lighys every evening. On one island, the light flashes every 45 seconds. The lighthouse on the second island has a light that       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 104964: Three lighthouses on three nearby islands flash their lighys every evening. On one island, the light flashes every 45 seconds. The lighthouse on the second island has a light that flashes every 2 minutes. The third lighthouse flashes a light ecery 1 1/4 minutes. Suppose all thr light flash together at 8:35 p.m.

At what time will all three lights flash together again?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Convert all of the time to seconds so you have the same units.
P1 = 45 seconds
P2 = 2 minutes = 120 seconds
P3 = 1 1/4 minutes = 75 seconds
This problem is similar to finding the least common multiple (LCM) for a fraction.
Break the numbers into their prime factors.
Find the largest powers of each prime factor.
Calculate the product of all of the largest powers of the prime factors.
45=highlight%283%5E2%29%2A5%5E1
120=highlight%282%5E3%29%2A3%5E1%2A5%5E1
75=3%5E1%2Ahighlight%285%5E%282%29%29
The prime factors are 2,3,and 5 with the highest power highlighted.
LCM+=+highlight%282%5E3%29%2Ahighlight%283%5E2%29%2Ahighlight%285%5E2%29
LCM+=+8%2A9%2A25
LCM = 1800 seconds. So every 1800 seconds after 8:35 PM, the lights will all blink simultaneously.
1800 seconds = 30 minutes
8:35 PM + 30 minutes = 9:05 PM.