A gardener can care for the Green’s property in 5 hours. If his helper assists him, they can complete the job in 4 hours. How long will it take the helper to do the job?
The correct answer and explanation is:
✅ Correct Answer: 20 hours
🧠Explanation:
This is a work-rate problem, which can be solved using the formula: Work=Rate×Time\text{Work} = \text{Rate} \times \text{Time}
We assume the total job (caring for the Green’s property) is 1 complete job.
Step 1: Define variables
- Let the gardener’s rate be 15\frac{1}{5} (since he can do 1 job in 5 hours).
- Let the helper’s rate be 1x\frac{1}{x} (since we don’t know how long it takes him alone).
- Working together, their combined rate is 14\frac{1}{4} (they finish in 4 hours together).
Step 2: Set up the equation
Gardener’s rate+Helper’s rate=Combined rate\text{Gardener’s rate} + \text{Helper’s rate} = \text{Combined rate} 15+1x=14\frac{1}{5} + \frac{1}{x} = \frac{1}{4}
Step 3: Solve the equation
Subtract 15\frac{1}{5} from both sides: 1x=14−15\frac{1}{x} = \frac{1}{4} – \frac{1}{5}
Find a common denominator: 14−15=5−420=120\frac{1}{4} – \frac{1}{5} = \frac{5 – 4}{20} = \frac{1}{20}
So, 1x=120⇒x=20\frac{1}{x} = \frac{1}{20} \Rightarrow x = 20
✅ Final Answer:
The helper can do the job alone in 20 hours.
📚 Why this works:
This problem uses the idea that when people work together, their rates add up. The gardener does part of the job per hour, and so does the helper. Adding those parts gives you the full job done in less time. By isolating the helper’s rate, we can find how long it would take him on his own to complete the entire task.
This concept is commonly tested in math for teamwork, time management, and efficiency modeling.