Answer: It will take 36 minutes(0.6 hour) until both ferries depart from their docks at the same time again.
Step-by-step explanation:
Given : Ferry A departs every 1.2 hours.
Ferry B departs every 1.8 hours.
To find : Time taken by both ferries until they depart from their docks at the same time again.
= LCM (1.2, 1.8) hours [LCM= Least common multiple]
= LCM (1.2(60 minutes), 1.8(60 minutes)) [Since 1 hour = 60 minutes]
= LCM (72 minutes, 108 minutes)
72 = 2 x 2 x 2 x 3 x 3 , 108 = 3 x 3 x 3 x 2 x 2
LCM (72,108) =2 x 2 x 3 x 3 =36
So, it will take 36 minutes until both ferries depart from their docks at the same time again.
In hour = [tex]\dfrac{36}{60}\text{ hour}=0.6\text{ hour}[/tex]
