QuestionIf Bus A takes 22 minutes and Bus B takes 15 minutes, when will they arrive together after leaving at 8:30 a.m.?
Studdy Solution
STEP 1
Assumptions1. Bus A takes22 minutes to complete its route. Bus B takes15 minutes to complete its route3. Both buses leave the station at830 a.m.
4. The buses continue to run their routes without stopping indefinitely5. We are looking for the time when both buses arrive at the station simultaneously after830 a.m.
STEP 2
We need to find the least common multiple (LCM) of the two bus routes' durations. The LCM will give us the time in minutes after both buses leave the station when they will arrive back at the same time.
STEP 3
To find the LCM of22 and15, we can use the prime factorization method. First, we find the prime factors of22 and15.
Prime factors of222,11Prime factors of153,5
STEP 4
Now, we take the highest power of all the primes that appear in the factorization of22 and15 to find the LCM.
STEP 5
Calculate the LCM.
STEP 6
The LCM we found is in minutes. This means that both buses will arrive at the station at the same time330 minutes after they leave the station at830 a.m.
STEP 7
To find the time of day when this occurs, we add330 minutes to30 a.m.First, convert330 minutes to hours and minutes. There are60 minutes in an hour, so we divide330 by60.
STEP 8
Calculate the hours and remaining minutes.
STEP 9
Now, add these5 hours and30 minutes to the initial time of830 a.m.
STEP 10
Calculate the arrival time.
Both buses will arrive at the station at the same time at200 p.m.
Was this helpful?
