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The time taken to complete a journey halves as the speed doubles - OCR - GCSE Maths - Question 4 - 2023 - Paper 6
Question 4
The time taken to complete a journey halves as the speed doubles. On the axes below, sketch a graph to show this relationship. It takes 40 minutes to fill a garde... show full transcript
Worked Solution & Example Answer:The time taken to complete a journey halves as the speed doubles - OCR - GCSE Maths - Question 4 - 2023 - Paper 6
Step 1
Sketch the Graph
Answer
To illustrate the relationship between time taken and speed, the graph will display a curve that shows that as speed increases (to the right), the time taken decreases (going down). The curve should not touch the axes, indicating that time cannot be zero at infinite speed and vice versa.
The graph will start high on the y-axis (time) and approach the x-axis (speed) without touching either.
Step 2
Calculate Time with 2 Hose Pipes
Answer
The time taken to fill the garden pond with 5 hose pipes is 40 minutes. If the flow rate from each hose pipe is the same, then using 2 hose pipes would alter the time taken due to the reduced rate of flow.
Using the formula:
ext{Time} = rac{ ext{Time with 5 hoses} imes ext{Number of hoses}}{ ext{Number of used hoses}} = rac{40 ext{ minutes} imes 5}{2} = 100 ext{ minutes}Therefore, it would take 100 minutes to fill the same pond using 2 hose pipes.