Question

Hi Hope you are doing well, I have a question : Question : At a bus station buses begin their routes at 6:00 a.m. The schedule for the two buses is based on the time intervals listed below.Bus A has a long route and leaves every 75 minutesBus B has a short route and leaves every 15 minutes.What is the next time Bus A and Bus B will leave the bus will leave the bus station at the same time. Answer choices :A : 7:00 a.m. B : 7:50 a.m. C : 7:15 a.m. D : 8:30 a.m.thank you for your time and help!!!

Answer 1

7.15 am (option C)

Step-by-step explanation:

Time bus begin their routes = 6.00am

Time it takes Bus A to laeve = 75 minutes

Time it takes bus B to leave = 15 minutes

We need to find the lowest common multiple of both times

15 = 3 × 5

75 = 3 × 5 × 5

LCM = 3 × 5 × 5 = 75

The time bus A and B will leave the bus station both times = time it begins + the LCM

The time bus A and B will leave the bus station both times = 6.00am + 75 minutes

75 minutes in hours:

1 hour = 60 minues

75 minutes = 60 minutes + 15 minutes = 1 hour 15 minutes

The time bus A and B will leave the bus station both times = 6.00am + 1 hour 15 minutes

The time bus A and B will leave the bus station both times = 7.00am + 15 minutes

The time bus A and B will leave the bus station both times = 7.15 am (option C)