Higher June 2025 Paper 1 Q10
10. It takes 5 workers a total of 24 hours to build a wall 180 m long.
(a) The workers have enough materials left over to build a further 300 m of the same wall.
How long will it take 8 workers to build this 300 m of wall? [3]
How long will it take 8 workers to build this 300 m of wall? [3]
(b)
(i) What assumption have you made in answering part (a)? [1]
(ii) If your assumption is not correct, what effect would this have on your answer to part (a)? [1]
| Scheme | Marks | Comments | ||||||
|---|---|---|---|---|---|---|---|---|
| \(24 \times \frac{5}{8}\) or \((\div1.6)\) oe | M1 | A table method altering all 3 values in the same ratio at the same time is M0 M marks may be seen in either order e.g.
| ||||||
| \(\times\frac{300}{180}\) or \(\times\frac{5}{3}\) or \((\div0.6)\) oe | M1 | FT from M0 previously awarded Must be from use of 24 e.g. if this calculation is performed first e.g.
| ||||||
| = 25 (hours) | A1 | CAO |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (Number of metres per worker per hour =) \((180\div5)\div24\ (= 1{\cdot}5)\) | M1 | May be seen in stages |
| (Number of hours needed =) \(300 \div (((180\div5)\div24)\times8)\) \((= 300\div(1{\cdot}5\times8) = 300\div12)\) | M1 | |
| = 25 (hours) | A1 | CAO |
| Scheme | Marks | Comments |
|---|---|---|
| (b)(i) Reference to all workers working at the same rate (as before). Examples for E1: Working as hard (as the original 5) etc Work at constant/same pace or speed | E1 | Do not allow: Examples for E0: ‘each worker does the same amount of work’ ‘any reference to breaks cost/availability of materials and/or tools’ ‘all workers built the same amount of wall’ ‘that they will work continuously’ ‘the 8 workers will work in the same amount of time as the 5 workers’ |
| (b)(ii) Time or answer will change / increase / decrease dependent on (b)(i) | E1 | If no valid assumption is made, then this mark cannot be awarded. Cannot award E0 E1. |
| (5) |