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A bus timetable shows the following information - OCR - GCSE Maths - Question 4 - 2019 - Paper 4
Question 4
A bus timetable shows the following information. - A bus following route T leaves for the train station every 20 minutes. - A bus following route A leaves for the a... show full transcript
Worked Solution & Example Answer:A bus timetable shows the following information - OCR - GCSE Maths - Question 4 - 2019 - Paper 4
Step 1
When is the next time one of each bus is timetabled to leave at the same time?
Answer
To find the next time both buses leave together, we need to determine the least common multiple (LCM) of their departure intervals:
- The bus following route T leaves every 20 minutes.
- The bus following route A leaves every 18 minutes.
First, let's find the LCM of 20 and 18:
The prime factorization of each number is:
- 20 = 2^2 × 5
- 18 = 2 × 3^2
The LCM is found by taking the highest power of each prime that appears:
Thus, the LCM is 180 minutes. This means both buses will leave at the same time every 180 minutes.
Starting from 8:37 am:
- Adding 180 minutes (or 3 hours), we arrive at:
- 8:37 am + 3 hours = 11:37 am
Therefore, the next time both buses leave together is at 11:37 am.
Step 2
Write down one assumption that was necessary to solve this problem.
Answer
One assumption is that the bus schedules do not change, meaning that the buses leave at consistent intervals and do not cancel any trips. Additionally, it is assumed that both buses are available for every departure time, allowing for synchronized timing.