Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?
Understand the Problem
The question is asking for the ratio of work capacity between men and women based on the number of days they take to complete the same work. We will analyze the work done by women and men over a certain period to find the required ratio.
Answer
The ratio of work capacity between men and women is given by the formula $ \frac{x}{y} = \frac{W}{M} $.
Answer for screen readers
The ratio of work capacity between men and women is given by:
$$ \frac{x}{y} = \frac{W}{M} $$
Steps to Solve
- Identify Work Completion Days for Men and Women
Assuming men take $M$ days to complete a certain work and women take $W$ days to complete the same work. We will denote:
- Work done by 1 man in 1 day as $x$.
- Work done by 1 woman in 1 day as $y$.
- Calculate Total Work Done
Total work done by men can be represented as:
$$ \text{Total work by men} = M \cdot x $$
Total work done by women can be represented as:
$$ \text{Total work by women} = W \cdot y $$
Since both groups complete the same work, we set the equations equal:
$$ M \cdot x = W \cdot y $$
- Find the Ratio of Work Capacity
To find the ratio of work capacity between men and women, we can express $x$ and $y$ in terms of the total work. From the above equation, we rearrange to find:
$$ \frac{x}{y} = \frac{W}{M} $$
- Final Ratio Representation
Thus, the ratio of work capacity of men to women can be expressed as:
$$ \frac{x}{y} = \frac{W}{M} $$
This means for every unit of work a woman does in one day, men will take a different proportion of days based on their work completion time.
The ratio of work capacity between men and women is given by:
$$ \frac{x}{y} = \frac{W}{M} $$
More Information
This result means that if you know how long men and women take to complete the same work, you can easily calculate how much work each can do in comparison. This ratio helps in understanding efficiency and productivity differences in various contexts.
Tips
- Confusing the days taken with work capacity: Remember that taking more days means less work capacity, not more.
- Mixing up the ratio direction: Ensure that the ratio is in the form of work done by men to work done by women.
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