At a railway station, trains are either eastbound or westbound - OCR - GCSE Maths - Question 3 - 2019 - Paper 4
Question 3
At a railway station, trains are either eastbound or westbound.
An eastbound train leaves the station every 25 minutes.
A westbound train leaves the station every 45... show full transcript
Worked Solution & Example Answer:At a railway station, trains are either eastbound or westbound - OCR - GCSE Maths - Question 3 - 2019 - Paper 4
Step 1
Find the time intervals for the trains
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Answer
The eastbound train leaves every 25 minutes and the westbound train leaves every 45 minutes.
Step 2
Calculate the Least Common Multiple (LCM)
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Answer
To determine when both trains leave together, we need to find the LCM of 25 and 45.
The prime factorization of 25 is: 52.
The prime factorization of 45 is: 32×5.
The LCM is calculated by taking the highest power of all prime factors: LCM=32×52=225.
Step 3
Convert the LCM into hours and minutes
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Answer
225 minutes can be converted into hours and minutes:
225 minutes = 3 hours and 45 minutes.
Step 4
Calculate the next time both trains leave
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Answer
Since both trains leave at 8am, adding 3 hours and 45 minutes to 8am gives:
8:00 am + 3 hours 45 minutes = 11:45 am.
Step 5
Final answer
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Answer
The next time the eastbound and westbound trains leave the station together is at 11:45 am.
