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Sam drives his car on a journey - Edexcel - GCSE Maths - Question 4 - 2021 - Paper 2
Question 4
Sam drives his car on a journey. Here is the travel graph for the first 15 minutes of his journey. Distance travelled (kilometres) 0 10 20 30 40 50 10:00 10... show full transcript
Worked Solution & Example Answer:Sam drives his car on a journey - Edexcel - GCSE Maths - Question 4 - 2021 - Paper 2
Step 1
Work out Sam's speed, in km/h, for the first 15 minutes of his journey.
Answer
To find Sam's speed, we first need to calculate the distance he travelled in the first 15 minutes. From the graph, it can be observed that Sam travelled 25 km in 15 minutes.
To calculate speed, we use the formula:
ext{Speed} = rac{ ext{Distance}}{ ext{Time}}Here, the time is 15 minutes, which we convert to hours:
ext{Time in hours} = rac{15}{60} = 0.25 ext{ hours}Now substituting the values into the speed formula:
ext{Speed} = rac{25 ext{ km}}{0.25 ext{ hours}} = 100 ext{ km/h}Therefore, Sam's speed for the first 15 minutes is 100 km/h.
Step 2
On the grid, complete the travel graph for Sam's journey.
Answer
At 10:15, Sam stops for 10 minutes, so there will be a horizontal line from 10:15 to 10:25, remaining at 25 km.
After the stop, he drives for 20 minutes at a speed of 75 km/h. The distance he covers in that time can be calculated as follows:
ext{Distance} = ext{Speed} imes ext{Time} = 75 ext{ km/h} imes rac{1}{3} ext{ hours} = 25 ext{ km}Adding this distance to the previous 25 km brings his total distance to:
So, he will drive from 10:25 to 10:45, reaching 50 km at 10:45. The graph should include:
- A horizontal line from (10:15, 25) to (10:25, 25).
- A straight line from (10:25, 25) to (10:45, 50).
This completes the travel graph for Sam's journey.