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Trams to the airport leave every 50 minutes - OCR - GCSE Maths - Question 21 - 2023 - Paper 1

Question 21

Trams to the airport leave every 50 minutes. Trams to the beach leave every 35 minutes. A tram to the airport and a tram to the beach leave together at 9:30 am. Whe... show full transcript

Worked Solution & Example Answer:Trams to the airport leave every 50 minutes - OCR - GCSE Maths - Question 21 - 2023 - Paper 1

Step 1

Find the Least Common Multiple (LCM)

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Answer

To determine when both trams will leave together again after 9:30 am, we first need to find the least common multiple (LCM) of the two departure intervals: 50 minutes and 35 minutes.

Calculating the LCM:

Prime factorization of 50:
- $50 = 2 \times 5^2$
Prime factorization of 35:
- $35 = 5 \times 7$
The LCM is found by taking the highest powers of all prime factors:
- LCM = $2^1 \times 5^2 \times 7^1 = 2 \times 25 \times 7 = 350$ minutes.

Step 2

Calculate the Next Departure Time

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Answer

Now, we add the 350 minutes to the initial departure time of 9:30 am.

First, converting 350 minutes into hours and minutes:

$350 \div 60 = 5$ hours and $50$ minutes.

Next, we add this to 9:30 am:

9:30 am + 5 hours = 2:30 pm
2:30 pm + 50 minutes = 3:20 pm.

Thus, the next time that both trams leave together is at 3:20 pm.

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