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The pie chart shows how Jack spent his time one evening - OCR - GCSE Maths - Question 10 - 2019 - Paper 1
Question 10
The pie chart shows how Jack spent his time one evening. (a) On which activity did Jack spend most time? (b) Jack says I spent \( \frac{1}{3} \) of my time on Gami... show full transcript
Worked Solution & Example Answer:The pie chart shows how Jack spent his time one evening - OCR - GCSE Maths - Question 10 - 2019 - Paper 1
Step 1
Step 2
Jack says I spent \( \frac{1}{3} \) of my time on Gaming. Show that he is not correct.
Answer
To assess Jack's claim, we first calculate the fraction of time he spent on Gaming based on the pie chart.
The total angle in the pie chart is 360°. Jack spent 150° on Gaming. We can find the fraction as follows:
[ \text{Fraction of time on Gaming} = \frac{150°}{360°} = \frac{15}{36} = \frac{5}{12} ]
Since ( \frac{5}{12} ) is not equal to ( \frac{1}{3} ) (which is ( \frac{4}{12} )), we conclude that Jack's assertion is incorrect, as ( \frac{5}{12} > \frac{1}{3} ).
Step 3
Find the time, in hours and minutes, that Jack spent reading.
Answer
The pie chart indicates that it represents 5 hours in total. Next, we need to determine the angle for Reading, which is 30°.
To find the time spent reading, we can calculate the fraction of time:
[ \text{Fraction of time on Reading} = \frac{30°}{360°} = \frac{1}{12} ]
Now, we multiply this fraction by the total time:
[ \text{Time on Reading} = \frac{1}{12} \times 5 \text{ hours} = \frac{5}{12} \text{ hours} ]
Converting ( \frac{5}{12} ) hours into minutes:
[ \frac{5}{12} \times 60 \text{ minutes} = 25 \text{ minutes} ]
Hence, Jack spent 0 hours and 25 minutes reading.