Question

Edward and klara are both nurses who are good friends with each other. Edward works at brigade hospital, where, in every 10 day cycle, he works the first 7 days and has three days off. Klara works at cedar mountain hospital, where, in every 7 day cycle, she works the first 5 days, and has 2 days off. Assume that both start their respective cycles on day 1 of week 1. In which weeks do they have the same two days off?

Answer 1

Answer:

So in week 7 & week 10 they have same two days off

Step-by-step explanation:

Edward and klara are both nurses who are good friends with each other. Edward works at brigade hospital, where, in every 10 day cycle, he works the first 7 days and has three days off. Klara works at cedar mountain hospital, where, in every 7 day cycle, she works the first 5 days, and has 2 days off. Assume that both start their respective cycles on day 1 of week 1. In which weeks do they have the same two days off?

Edward has  3 days off after 7 days working in 10 days cycle

3 days before completion of cycle

so Edward off days are

10n-2, 10n-2 , 10n    where n ≥1

Klara has 2 days off after 5 days working in 7 days cycle

2 days before completion of cycle

so klara off days are

7m-1 , 7m  where m ≥1

As they started on same day

so 7m-1 should equal to 10n-2 , or 10n-1 to have same two days off

Case 1

7m-1 = 10n-2

=> 7m = 10n-1

This equation will hold true for m = 7  & n = 5

this mean 48th & 49th days are off for both (week 7)

Case 2

7m-1 = 10n-1

=> 7m = 10n

This will hold true for m = 10 & n = 7

this mean 69th & 70th days are off for both (week 10)

So in week 7 & week 10 they have same two days off