Final answer:
The earliest time all three nurses will call a new patient simultaneously is at 9:00 A.M., which is found by calculating the least common multiple of the average times (6, 8, 10 minutes) they each spend with a patient, resulting in 120 minutes, or 2 hours after 7:00 A.M.
Step-by-step explanation:
To find when all three triage nurses in the ER will call a new patient again at the same time, we need to determine the least common multiple (LCM) of their individual times spent with each patient (6, 8, and 10 minutes). This calculation will give us the first time they all coincide after 7:00 A.M.
Firstly, we determine the prime factors of each time interval:
- 6 = 2 × 3
- 8 = 23
- 10 = 2 × 5
Now we identify the highest power of each prime number that appears in this factorization and multiply them together to find the LCM:
LCM = 23 × 3 × 5 = 8 × 3 × 5 = 120 minutes
Since 120 minutes is equivalent to 2 hours, if the nurses start calling patients at 7:00 A.M., they will all call a new patient at the same time again 2 hours later, which is at 9:00 A.M.
The correct answer is B) 9:00 A.M.