Foundation November 2019 Paper 2 Q13
13.
(a)
A train from Leicester to London has:
- 1 first class carriage with 48 seats,
- 4 standard class carriages, each with 72 seats.
The train manager notes that:
- \(\frac{3}{4}\) of the first class seats are taken,
- \(\frac{5}{8}\) of the standard class seats are taken,
- no passengers are standing.
The train manager thinks that the train is more than \(\frac{2}{3}\) full.
Is the train manager correct?
You must show all your working. [7]
Tick (✓) the appropriate box.
The train manager is correct ☐ The train manager is not correct ☐
(b)
The distance by rail from Leicester to London is 100 miles.
(i)
Assume that the train travels at an average speed of 80 mph.
Calculate the arrival time in London of a train that leaves Leicester at 11:50 a.m. [3]
(ii) The train actually travelled slower than the assumed 80 mph.
How would this affect the arrival time? [1]
How would this affect the arrival time? [1]
| Scheme | Marks | Comments |
|---|---|---|
| 3 × 48 ÷ 4 (36) | M1 | Watch out for alternative methods referring to seats empty. This is 12 seats instead of 36, 108 seats instead of 180 and 120 seats instead of 216. Must state that these are empty seats. |
| + 4 × 72 ÷ 8 × 5 (180) | M1 | |
| (36 + 180) = 216 | A1 | |
| (Total train capacity is) 1 × 48 + 4 × 72 | M1 | |
| = 336 | A1 | |
| (\(\frac{2}{3}\) of 336 =) 224 or (216/336 =) 0.64(…) or 64(.28…)% AND indicates that the train manager is not correct | B2 | FT ‘their derived 336’ B1 for sight of \(\frac{2}{3}\) of 336 or 216/336 or 224 or 0.64(…) or 64(.28…)% Note that a common error is to use only 1 standard carriage instead of 4. In this case, their 336 would be 120, Their 224 would be 80, Their 216 would be 81, Therefore, the train manager would be CORRECT. Candidates can get B1 for these numbers seen, and B2 if their decision is correct. |
Corrected by Westie's Workshop
- The board's mark scheme printed “48 seats instead of 216”. Changed to “120 seats instead of 216” because the empty seats are 12 + 108 = 120 (that is 336 − 216), not 48.
Original: see the board's mark scheme PDF (link above).
| Scheme | Marks | Comments |
|---|---|---|
| (i) Time = 100 ÷ 80 (= 1.25 hrs) | M1 | |
| 11:50 + 1hr 15 mins | m1 | FT ‘their 100 ÷ 80’ Allow for 1.25 hours or 1 hr 25 mins |
| (Arrival time) 13(:)05 or 1(:)05 p.m. | A1 | CAO. Allow 1(:)05 or 13(:)05(pm) |
| (ii) Affect, e.g. ‘The arrival time would be later’ | E1 | Accept, e.g. ‘the journey would take longer’ or ‘it would be later’ but do not accept ‘it would be longer’ |
| (11) |