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Viraj cycled from his home to visit his aunt - OCR - GCSE Maths - Question 17 - 2018 - Paper 1
Question 17
Viraj cycled from his home to visit his aunt. He drew this graph to show his journey. He stopped at a shop 7 km from his home. (c) Work out Viraj's average speed be... show full transcript
Worked Solution & Example Answer:Viraj cycled from his home to visit his aunt - OCR - GCSE Maths - Question 17 - 2018 - Paper 1
Step 1
(c) Work out Viraj's average speed between his home and the shop.
Answer
To calculate Viraj's average speed, we need to use the formula for speed:
ext{Speed} = rac{ ext{Distance}}{ ext{Time}}From the graph, we see that Viraj cycled 7 km to the shop. We need to convert this distance to meters:
Next, we look at the time he took to travel this distance. Referring to the graph, we can observe that he took 12 minutes to cycle from home to the shop.
Now we can compute the speed:
ext{Speed} = rac{7000 ext{ meters}}{12 ext{ minutes}} \n= rac{7000}{12} ext{ meters per minute} \n ext{Speed} ightarrow 583.33 ext{ m/min (approximately)}Thus, the average speed between his home and the shop is approximately 583.33 metres per minute.
Step 2
(d) How can you tell, without doing any calculations, that Viraj's average speed between his home and the shop is greater than his average speed between the shop and his aunt?
Answer
We can analyze the graph visually. The portion of the graph representing the journey from home to the shop is steeper than that from the shop to the aunt's house. A steeper slope indicates a greater speed, suggesting that Viraj cycled faster to the shop than to his aunt. Therefore, we can conclude that his average speed between home and the shop is greater than that between the shop and his aunt.