As Simi budgets her household's water use, she fills a garden butt from a hose. The graph shows the volume of water, in litres, in the butt over time. 04812...
Question 1 Report
As Simi budgets her household's water use, she fills a garden butt from a hose. The graph shows the volume of water, in litres, in the butt over time.
- Write down the time at which the rate of filling changes. (1)
- Work out the rate of filling before this time. (2)
- Work out the rate of filling after this time. (2)
Answer Details
The volume of water rises steadily while the hose fills the butt, but the rate of filling changes at the point where the graph's slope changes, most likely because the hose flow was adjusted or the butt's shape narrows.
(a) The graph changes gradient at \(t = 10\) minutes. [1 mark]
(b) Before this time, the volume rises from 0 litres to 40 litres in 10 minutes:
\[\frac{40 - 0}{10 - 0} = 4 \text{ litres per minute}\] [2 marks]
(c) After this time, the volume rises from 40 litres to 100 litres over the remaining 6 minutes (from \(t=10\) to \(t=16\)):
\[\frac{100 - 40}{16 - 10} = 10 \text{ litres per minute}\] [2 marks]
Exam tip: a change in gradient partway along a graph always signals a change in rate; treat each straight section separately and use only the two endpoints of that section in the calculation.
Download The App On Google Playstore
Everything you need to excel in your exams
