QuestionYou and your brother work from 4 PM to midnight. You have every 9th night off, he has every 6th. When is your next shared night off after April 1?
Studdy Solution
STEP 1
Assumptions1. You have every ninth night off.
. Your brother has every sixth night off.
3. Both of you were off on April1.
4. We need to find the next date when both of you have the same night off.
STEP 2
Since you are off every ninth night and your brother is off every sixth night, the next night when both of you will be off will be the least common multiple (LCM) of6 and9.
STEP 3
To find the LCM of6 and9, we first list the prime factors of each number.
For6, the prime factors are2 and3.
For9, the prime factors are3 and3.
STEP 4
The LCM is found by multiplying each factor the greatest number of times it occurs in either number. In this case, the LCM is2*3*3.
STEP 5
Calculate the LCM.
STEP 6
The LCM of6 and9 is18, which means you and your brother will both be off on the18th night after April1.
STEP 7
To find the date18 days after April1, we simply add18 to the date of April1.
STEP 8
Calculate the date.
You and your brother will both have the same night off again on April19.
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