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Three people take $2\frac{1}{2}$ hours to deliver leaflets to 270 houses - OCR - GCSE Maths - Question 3 - 2020 - Paper 1
Question 3
Three people take $2\frac{1}{2}$ hours to deliver leaflets to 270 houses. Assuming all people deliver leaflets at the same rate, how long will it take five people t... show full transcript
Worked Solution & Example Answer:Three people take $2\frac{1}{2}$ hours to deliver leaflets to 270 houses - OCR - GCSE Maths - Question 3 - 2020 - Paper 1
Step 1
Calculate time taken for one person to deliver leaflets to 270 houses
Answer
First, we will convert the mixed number time into an improper fraction. The time taken for three people is hours, which equals ( \frac{5}{2} ) hours.
To find the time for one person, we divide this time by the number of people: [ ext{Time for one person} = \frac{\frac{5}{2}}{3} = \frac{5}{6} \text{ hours} ]
Step 2
Calculate the total time taken for one person to deliver leaflets to 405 houses
Answer
Next, we calculate the time taken by one person to deliver leaflets to 405 houses. The rate of delivery can be found as follows:
[ \text{Rate} = \frac{270 \text{ houses}}{\frac{5}{2} \text{ hours}} = \frac{270 \times 2}{5} = \frac{540}{5} = 108 \text{ houses per hour} ]
Now, we calculate how long it takes to deliver leaflets to 405 houses: [ \text{Time for one person} = \frac{405 \text{ houses}}{108 \text{ houses per hour}} = \frac{405}{108} \text{ hours} = \frac{15}{4} \text{ hours} = 3.75 ext{ hours} ]
Step 3
Calculate time for five people to deliver leaflets
Answer
Finally, we find how long it would take for five people to deliver the same amount of leaflets: [ \text{Time for five people} = \frac{3.75 ext{ hours}}{5} = 0.75 ext{ hours} ]
To convert this into hours and minutes: [ 0.75 \text{ hours} = 0 \text{ hours} + 0.75 \times 60 ext{ minutes} = 45 ext{ minutes} ]
Thus, the final answer is 0 hours and 45 minutes.