A can do 20% of a job in 7 days and B can do 25% of the job in 7 days if they worked alone. How much of the job (in percentage) can they complete in 7 days if they worked together?
45%
Understanding Work and Time Problem
This question asks us to determine the combined percentage of a job that two individuals, A and B, can complete in a specific time period (7 days), given the percentage of the job each can complete individually in the same time period.
Analysing Individual Work Rates
We are given the following information:
- A can do 20% of the job in 7 days when working alone.
- B can do 25% of the job in 7 days when working alone.
The question specifically asks how much of the job they can complete together in 7 days. Since the time period is the same for both individuals and for the combined work, we can simply add the percentages of the job they complete individually within that time frame.
Calculating Combined Work in 7 Days
To find the total percentage of the job they complete together in 7 days, we add the percentage of work A does in 7 days and the percentage of work B does in 7 days.
Combined work in 7 days = Work done by A in 7 days + Work done by B in 7 days
Combined work in 7 days = $$20\% + 25\%$$
Combined work in 7 days = $$45\%$$
Therefore, if A and B work together, they can complete 45% of the job in 7 days.
Summary of Calculations
Here is a quick summary:
- A's work in 7 days = 20%
- B's work in 7 days = 25%
- Combined work in 7 days = $$20\% + 25\% = 45\%$$
The percentage of the job they can complete together in 7 days is 45%.
Revision Table: Work and Time Concepts
| Concept | Explanation | Formula (Example: A does work in D days) |
|---|---|---|
| Work Rate | The amount of work done per unit of time. | If A completes $$1$$ job in $$D$$ days, A's daily work rate is $$\frac{1}{D}$$ job per day. |
| Total Work | Usually considered as 1 unit or 100%. | Work = Rate × Time |
| Combined Work Rate | Sum of individual work rates. | If A's rate is $$R_A$$ and B's rate is $$R_B$$, combined rate is $$R_A + R_B$$. |
| Time to Complete Together | Time taken by individuals working together to complete the total work. | Time = $$\frac{\text{Total Work}}{\text{Combined Rate}}$$ |
Additional Information: Work and Time Problems
Work and time problems often involve calculating the time taken to complete a task based on individual work rates. The fundamental principle is that the total work done is the product of the work rate and the time spent working. Work rates are usually expressed as the fraction or percentage of work done per unit of time (e.g., per day, per hour).
Key Principles:
- Work Rate and Time are Inversely Proportional: If a person works faster (higher rate), they take less time to complete the same amount of work, and vice versa.
- Adding Work Rates: When individuals work together, their work rates add up to find the combined work rate, assuming they work independently without affecting each other's pace.
- Consistency of Units: Ensure that the units of work and time are consistent throughout the calculation. If the rate is per day, the time should be in days.
In this specific problem, since the time period (7 days) was fixed and the same for individual and combined work, we could directly add the percentages of work completed. If the question had asked for the time taken to complete the *entire* job (100%) together, we would first calculate their daily work rates from the given information and then use the combined daily rate to find the total time.
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