Question

Lars, Rita and Alan regularly go swimming. Lars goes every

2 days, Rita goes every 3 days and Alan goes every 5 days.
They all went swimming together on Friday 1st June.
a) On what date will Lars and Rita next go swimming together?
b) On what date will Rita and Alan next go swimming together?
c) On what day of the week will all 3 next go swimming together?
d) Which of the 3 (if any) will go swimming on 15th June?

Answer 1

Part (a)

• Lars goes every 2 days
• Rita goes every 3 days

The LCM of 2 and 3 is 2*3 = 6.

Lars and Rita's schedule aligns every 6 days.

These two went swimming together on June 1st.

6 days later would be June 7th, which is when they swim together again. See the chart in part (d) below.

Answer: June 7th

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Part (b)

• Rita goes every 3 days
• Alan goes every 5 days.

LCM = 3*5 = 15

Add 15 days to the first of June to get 1+15 = 16. See the chart in part (d) below.

Answer: June 16th

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Part (c)

The LCM of 2, 3, and 5 is 2*3*5 = 30

The trio will swim together every 30 days.

Since there are 7 days in a week, divide 30 over 7 and find the remainder.

30/7 = 4 remainder 2

We don't care about the quotient. All we focus on is the remainder.

A remainder of 2 means that we move 2 days ahead of Friday to land on Sunday. You can use a calendar to confirm that adding 30 days to the starting Friday will get you to Sunday. It doesn't matter what month you are in, so it could be June or any month really.

Answer: Sunday

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Part (d)

Here's a chart when all three go swimming:

`\begin{array} \cline{1-3}\text{Lars} & \text{Rita} & \text{Alan}\\\cline{1-3}1 & 1 & 1\\\cline{1-3}3 & 4 & 6\\\cline{1-3}5 & 7 & 11\\\cline{1-3}7 & 10 & 16\\\cline{1-3}9 & 13 & 21\\\cline{1-3}11 & 16 & 26\\\cline{1-3}13 & 19 & 31\\\cline{1-3}15 & 22 & 36\\\cline{1-3}\end{array}`

Each number refers to a day number in June, with exception to the 36 for Alan. Treat that "36" as 36-30 = 6 days beyond the end of June (aka July 6th).

Each person starts at 1. Lars will involve adding 2 to each item. Rita has +3 to each item. Alan has +5 to each item. That chart shows "15" only in the Lars column.

Answer: Lars only