A medium question on ratios for P5–P6, with a step-by-step solution, diagrams and the answer. Ratio questions appear in the Hua Xia Cup's P4 to P6 first rounds, qualifying rounds and finals, such as linked ratios and ratios that change.
The question
A community centre is packing a batch of gift bags for elderly residents.
The plan was for 6 volunteers to do it, taking 6 hours.
Every volunteer packs the same number of bags each hour.
On the day, only 4 volunteers came, and those 4 worked from start to finish.
How many hours longer than planned did the job take?
Show the hints (2)
💡Hint 1: If there were just one volunteer, how many hours would it take?
💡Hint 2: The whole job is the same. How long would 4 take?
Worked solution
Have a go first, then read the solution step by step.
1.Call one volunteer's work in one hour 1 part. The plan was 6 people for 6 hours, so the whole job = 6 × 6 = 36 parts.
2.The job is still 36 parts. 4 people do 4 parts each hour, so they need 36 ÷ 4 = 9 hours.
3.9 − 6 = 3: 3 hours longer.
⚠️Common mistake: thinking 2 fewer people means 2 hours more. More people take less time: if the numbers of people are 6 : 4, the times are 4 : 6.
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