AQA GCSE Mathematics Paper 2 (Higher), June 2025: Question 13

4 marks · Medium difficulty · Multi-step Problem

Determine whether Emma or Chan takes less time to complete a 154-mile journey, given their respective speeds across different sections of the journey.

Practise this question

Question

Question 13 states: Emma and Chan each drive 154 miles from A to B. Emma drives the whole way at an average speed of 56 miles per hour. Chan drives 85 miles at an average speed of 50 miles per hour, and then the rest of the way at an average speed of 60 miles per hour. Who takes less time, Emma or Chan? Show working to support your answer. The question is worth 4 marks.

Mark scheme

Show the mark scheme Mark scheme for Question 13 showing two alternative methods. Alternative method 1 calculates total times: 154 divided by 56 gives 2.75 hours or 2 h 45 min (M1); 85 divided by 50 gives 1.7 hours (M1); adding (154 - 85) divided by 60 gives total time 2.85 hours or 2 h 51 min (M1dep); concluding 2.75 and 2.85 and Emma (A1). Alternative method 2 compares average speeds: Chan's total time is found as 2.85 hours (M1, M1dep), Chan's overall average speed is 154 divided by 2.85 which is approximately 54.04 mph (M1dep), and Emma with 56 mph is faster so takes less time (A1).

How to answer it

Multi-Stage Speed, Distance & Time

📌 What this question tests

This 4-mark problem tests your ability to apply the compound measure formula Time = Distance ÷ Speed across single and multi-stage journeys, interpret decimal hours correctly without confusing them with minutes, and make a justified numerical comparison.

Question 13 Walkthrough (4 Marks)

Comparing journey times between Emma and Chan

💡 Key Formulae & Facts

  • Time = Distance ÷ Speed
  • Total Time for Split Journey: Must be calculated by finding the time for each individual leg and adding them together.
  • Decimal Time to Minutes: Multiply the decimal part by 60.
    e.g. 0.75 hours = 0.75 × 60 = 45 minutes.
    0.15 hours = 0.15 × 60 = 9 minutes.

🧠 Mark Scheme Breakdown

  • M1 : Correct method to find Emma's time ( 154 ÷ 56 ).
  • M1 : Correct method for Chan's 1st stage ( 85 ÷ 50 ).
  • M1 (dep) : Complete method for Chan's total time (adding stage 1 and stage 2 times).
  • A1 : Correct comparable times (e.g. 2.75 h vs 2.85 h) and stating Emma.

📐 Step-by-Step Calculations (Method 1: Comparing Total Time)

1 Calculate Emma's total journey time:

Distance = 154 miles, Speed = 56 mph
Time = 154 ÷ 56 = 2.75 hours (or 2 hours 45 minutes / 165 minutes)
[Awards the 1st M1 mark]

2 Calculate Chan's first leg time (85 miles at 50 mph):

Time₁ = 85 ÷ 50 = 1.7 hours (or 1 hour 42 minutes / 102 minutes)
[Awards the 2nd M1 mark]

3 Calculate Chan's remaining distance and second leg time:

Remaining distance = 154 - 85 = 69 miles
Speed = 60 mph
Time₂ = 69 ÷ 60 = 1.15 hours (or 1 hour 9 minutes / 69 minutes)

4 Calculate Chan's total time:

Total Time = 1.7 + 1.15 = 2.85 hours (or 2 hours 51 minutes / 171 minutes)
[Awards the 3rd M1 mark, dependent on previous method]

5 Compare times and state the conclusion:

2.75 hours < 2.85 hours (Emma took 0.1 hours / 6 minutes less).
Therefore, Emma takes less time.
[Awards the final A1 mark]

✅ Final Answer

Emma takes less time.

Full marks require supporting values in a matching unit:
• Decimal hours: 2.75 and 2.85
• Hours & minutes: 2 h 45 min and 2 h 51 min
• Minutes: 165 min and 171 min

❌ Common Calculation Traps

  • Averaging speeds directly: Calculating (50 + 60) ÷ 2 = 55 mph for Chan is completely wrong because he spends different amounts of time at each speed. You must find each leg's time separately.
  • Decimal hours misconception: Treating 2.75 hours as 2 hours 75 minutes, or 1.7 hours as 1 hour 7 minutes (or 1 hour 70 minutes). Leaving values in decimals (2.75 and 2.85) is the safest method.
  • Missing the comparison: Working out both times correctly but forgetting to write "Emma" on the answer line loses the final mark.

Topics

Ratio, proportion and rates of change · 3.3 Ratio, proportion and rates of change

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 2 (Higher), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.