At a bus station, buses begin their routes at 6.am. the schedule for two of the buses is based on time intervals listen below-
*bus a leaves every 75 minutes.
*bus b leaves every 15 minutes.
what is the next time bus and bus b will leave the bus station at the same time.
part b
it takes a steamboat 12 hours to travel 300 miles, how many miles does the steamboat travel per hour?

Part A: The two buses leave the bus station at 7 : 15 am

Part B: The steamboat travels 25 miles per hour

Step-by-step explanation:

* Lets explain how to solve the problem

Part A

- Buses begin their routes at 6 am at a bus station

- Bus A leaves every 75 minutes

- Bus B leaves every 15 minutes

- We want to know the next time Bus A and Bus B will leave the bus

  station at the Same time

# Bus A

∵ Bus A leaves every 75 minutes

- Lets change 75 minutes to hours and minutes

∵ 1 hour = 60 minutes

∴ 75 minutes = 75/60 = 5/4

- Change 5/4 to mixed number

∵ 5/4 = 1 1/4

∴ 75 minutes = 1 1/4 hours

- Lets change 1/4 hour to minutes

∴ 1/4 × 60 = 15 minutes

∴ 75 minutes = 1 hour and 15 minutes

∵ Bus A leaves the station at 6 am

- Add 1 hour and 15 minutes to that time

∵ 6 + 1 : 15 = 7 : 15

∴ Bus A leaves the station nest time at 7 : 15 am

# Bus B

∵ Bus B leaves every 15 minutes

∵ Bus B leaves the station at 6 am

- Add 15 minutes to 6 am

∴ Bus B leaves the station next time at 6 : 15 am

- Add another 15 minutes for next time

∴ Bus B leaves the station next time at 6 : 30 am

- Add another 15 minutes for next time

∴ Bus B leaves the station next time at 6 : 45 am

- Add another 15 minutes for next time

∵ 15 + 45 = 60 ⇒ add 6 by 1 because 60 minutes = 1 hour

∴ Bus B leaves the station next time at 7 am

- Add another 15 minutes for next time

∴ Bus B leaves the station next time at 7 : 15 am

- The 2 buses leave the station at the same time again at 7:15 am

* The two buses leave the bus station at 7 : 15 am

Part B

- It takes a steamboat 12 hours to travel 300 miles

- We need to find how many miles it travels per hour

∵ The steamboat travels 300 miles in 12 hours

- Divide the distance by the time to find its rate

∵ 300 ÷ 12 = 25

- That means it travels 25 miles per hour

∴ The steamboat travels 25 miles per hour

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.