### graph of running distance

Question Sample Titled 'graph of running distance'

The figure shows the graph of the distances travelled by Aidan and Lauren during their running practice in the afternoon.

Distance travelled ${\left(\text{m}\right)}$${4}:{00}$${4}:{14}$${4}:{20}$${4}:{25}$${4}:{40}$${0}$${2500}$LaurenAidanTime${A}$${B}$

 (a) Find the distance travelled by Lauren at ${4}:{10}$ in the afternoon. (2 marks) (b) At what time after ${4}:{00}$ in the afternoon do Aidan and Lauren first meet? (Give the answer correct the nearest minute.) (2 marks) (c) Aidan thinks that his average speed is higher than that of Lauren during the period ${4}:{00}$ to ${4}:{25}$ in the afternnon. Do you agree? Explain your answer. (2 marks)

 (a) Required distance $={\left(\dfrac{{2500}}{{25}}\right)}\times{10}$ 1M  $={1000}$ $\text{m}$ 1A  (b) Let they first meet after ${x}$ minutes from ${4}:{00}$.  ${\left(\dfrac{{2500}}{{25}}\right)}\times{x}$ $={2500}-\dfrac{{2500}}{{{40}-{20}}}\times{\left({x}-{20}\right)}$ 1M ${x}$ $=\dfrac{{200}}{{9}}$ ${x}$ $\approx{22}$ $\therefore$The first meet at ${4}:{22}$. 1A  (c) In the period, Aidan's total distance travelled $={2500}+\dfrac{{2500}}{{{40}-{20}}}\times{\left({25}-{20}\right)}$ 1M  $={3125}$ $\text{m}$ Lauren's total distance travelled $={2500}$ $\text{m}$ $\therefore$Aidan's travelled longer distance. Thus, his average speed is higher. 1A $\therefore$He is correct.

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