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At 5.45p.M .,lixin,khairul and Devil are at the starting point of a 1-km circular path. Lixin Takes 18 minutes to walk one round ,khairul needs 360 seconds to run 1 round ansd Devi cycles 2 rounds in 4 minutes .Find the time when all three of them will next meet

Sagot :

MrRoyalidn

Answer:

[tex]Meeting\ Time = 6:03\ pm[/tex]

Step-by-step explanation:

Given

[tex]Start\ Time= 5:45pm[/tex]

[tex]Lixin = 18\ min/round[/tex]

[tex]Khairul = 360\ seconds/round[/tex]

[tex]Devi = 4minutes/2\ rounds[/tex]

Required

Determine their next meeting time

First, we need to get their unit rate in minutes per round

[tex]Lixin = 18\ min/round[/tex]

[tex]Khairul = 360\ seconds/round[/tex]

Convert 360 seconds to minutes

[tex]Khairul = \frac{360}{60} min/round[/tex]

[tex]Khairul = 6 min/round[/tex]

[tex]Devi = 4minutes/2\ rounds[/tex]

Divide by 2/2

[tex]Devi = 2mins/round[/tex]

So, we have:

[tex]Lixin = 18\ min/round[/tex]

[tex]Khairul = 6 min/round[/tex]

[tex]Devi = 2mins/round[/tex]

Next, is to determine the LCM of 18, 6 and 2

[tex]18=2 * 3 * 3[/tex]

[tex]6 = 2 * 3[/tex]

[tex]3 = 3[/tex]

Their LCM is:

[tex]LCM = 2 * 3 * 3[/tex]

[tex]LCM = 18[/tex]

This means that they will meet 18 minutes after their initial time of departure.

So:

[tex]Meeting\ Time = 5:45\ pm + 18\ minutes[/tex]

[tex]Meeting\ Time = 6:03\ pm[/tex]

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