1MA0 Foundation June 2012 Paper 1 Q24
24 Buses to Acton leave a bus station every 24 minutes.
Buses to Barton leave the same bus station every 20 minutes.
A bus to Acton and a bus to Barton both leave the bus station at 9 00 am.
When will a bus to Acton and a bus to Barton next leave the bus station at the same time? (3)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| Acton after 24, 48, 72, 96, .. Barton after 20, 40, 60, 80, .. LCM of 20 and 24 is 120 9: 00 am + 120 minutes OR Acton after 24, 48, 1h 12 min... Barton after 20, 40, 1 h LCM is 2 hours 9: 00 am + 2 hours OR Times from 9: 00 am when each service leaves the bus station Acton at 9: 24, 9: 48, 10: 12.. Barton at 9: 20, 9: 40, 10: 00.. OR \(20 = 2 \times 2 \times 5\) \(24 = 2 \times 2 \times 2 \times 3\) \(2 \times 2 \times 2 \times 3 \times 5 = 120\) | 11: 00 am | 3 | M1 for listing multiples of 20 and 24 with at least 3 numbers in each list ; multiples could be given in minutes or in hours and minutes (condone one addition error in total in first 3 numbers in lists) A1 identify 120 (mins) or 2 (hours) as LCM A1 for 11: 00 (am) or 11(am) or 11 o'clock OR M1 for listing times after 9am when each bus leaves the bus station, with at least 3 times in each list (condone one addition error in total in first 3 times after 9am in lists) A1 for correct times in each list up to and including 11: 00 A1 for 11: 00 (am) or 11(am) or 11 o'clock OR M1 for correct method to write 20 and 24 in terms of their prime factors 2, 2, 5 and 2, 2, 2, 3 (condone one error) A1 identify 120 as LCM A1 for 11: 00 (am) or 11(am) or 11 o'clock |