Number 6
4 marks · NormalA factory produces toy cars. The number of workers n and the number of days d to complete an order are inversely proportional. An order takes 36 days with 5 workers.
How many days would it take 9 workers to complete the same order?
Write the formula connecting n and d.
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Show answer
(a) 20 days
(b) n × d = 180 or d = 180/n
Common mistakes: using direct instead of inverse proportion
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Sets up inverse proportion relationship: n × d = constant.
A1 (a) · 1 mark · Finds correct number of days for 9 workers (20 days).
M2 (b) · 1 mark · States or derives connection between n and d.
A2 (b) · 1 mark · Writes correct formula, n × d = 180 or d = 180/n.
Worked solution
n × d = constant. 5 × 36 = 180. For n = 9, d = 180/9 = 20 days. Formula: n × d = 180 or d = 180/n.