Question

Two ferries just departed from their docks at the same time. Ferry A departs every 1.2 hours. Ferry B departs every 1.8 hours. How long will it be until both ferries depart from their docks at the same time again?

Answer 1

Answer: It will take 36 minutes(0.6 hour) until both ferries depart from their docks at the same time again.

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 =
`(36)/(60)\text{ hour}=0.6\text{ hour}`