8 men and 12 women can build a wall in 10 days. 6 men and 8 women can build the same wall in 14 days. How long will it take for 1 woman to build it alone?
280 days
Wall Building Work Rate Problem
This problem involves calculating the time required for an individual (a woman) to complete a specific task (building a wall), based on information about combined efforts of groups of men and women over different time periods.
The core task is to determine the individual work contribution rate of men and women using the provided data.
Work Equations Setup
Let \(M\) denote the work rate of one man (amount of wall built per day) and \(W\) denote the work rate of one woman (amount of wall built per day). The total work required is building 1 wall.
We use the fundamental relationship: Work = Rate × Time.
Scenario 1: 8 men and 12 women build the wall in 10 days.
- Combined rate: \((8M + 12W)\)
- Time: \(10 \text{ days}\)
- Total Work: \(1 \text{ wall}\)
This translates to the equation:
\( (8M + 12W) \times 10 = 1 \)
Expanding this equation gives:
\( 80M + 120W = 1 \quad \text{(Equation 1)} \)
Scenario 2: 6 men and 8 women build the same wall in 14 days.
- Combined rate: \((6M + 8W)\)
- Time: \(14 \text{ days}\)
- Total Work: \(1 \text{ wall}\)
This translates to the equation:
\( (6M + 8W) \times 14 = 1 \)
Expanding this equation gives:
\( 84M + 112W = 1 \quad \text{(Equation 2)} \)
Individual Work Rates Calculation
We now have a system of two linear equations. Since both Equation 1 and Equation 2 represent the completion of the same single wall (equal to 1 unit of work), we can set the left-hand sides equal to each other:
\( 80M + 120W = 84M + 112W \)
To find the relationship between \(M\) and \(W\), we rearrange the terms:
\( 120W - 112W = 84M - 80M \)
\( 8W = 4M \)
Solving for \(M\) in terms of \(W\):
\( M = \frac{8W}{4} \)
\( M = 2W \)
This result indicates that one man's work rate is equivalent to the work rate of two women.
Now, substitute \(M = 2W\) back into Equation 1 to find the value of \(W\):
\( 80(2W) + 120W = 1 \)
\( 160W + 120W = 1 \)
\( 280W = 1 \)
This equation signifies that the combined effort of 280 women working together is required to complete the wall in one day. Thus, the work rate of a single woman is:
\( W = \frac{1}{280} \)
So, one woman completes \(1/280\) of the wall each day.
Time for One Woman Alone
To find the total time (\(T\)) it takes for one woman to build the entire wall by herself, we use the work formula again:
Work = Rate × Time
\( 1 = W \times T \)
Substitute the value of \(W\) we found:
\( 1 = \frac{1}{280} \times T \)
Now, solve for \(T\):
\( T = 1 \times 280 \)
\( T = 280 \)
Conclusion on Wall Building Time
Therefore, it will take one woman 280 days to build the wall alone.
Similar Questions
P is 30% more efficient than Q. How much time will they, working together, take to complete a job that P alone could have done in 23 days?
8 men and 12 women can build a wall in 10 days. 6 men and 8 women can build the same wall in 14 days. How long will it take for 2 women and 1 man to build it together?
If 6 men and 8 boys can do a piece of work in 10 days, while 26 men and 48 boys can do the same work in 2 days, then the time taken by 10 men and 20 boys for doing the same piece of work will be:
Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
8 men and 12 women can build a wall in 10 days. 6 men and 8 women can build the same wall in 14 days. How many more days will 1 woman take to build that wall alone compared to the number of days 1 man will take to build same wall alone?
48 men can do a work in 5 days while 40 women can do the same work in 9 days. In how many days can 4 men and 6 women together do the same work?
If 6 men and 8 boys can do a piece of work in 10 days, while 26 men and 48 boys can do the same work in 2 days, then the time taken by 20 men to do the same piece of work is:
A can complete a piece of work in 20 days and B can do the same work in 15 days. B worked alone for 6 days and left. In how many days can A complete the remaining work alone?
A and B can together complete a piece of work in 5 days. They worked together for 4 days, and then B left. After another 2 days, A completed the remaining work. In how many days can A complete the entire work alone?
6 men or 5 women can complete a job in 7 days. 6 men work for 5 days and leave. The number of women required to complete the remaining work in 5 days is:
Important Questions from Time and work
A person can complete 20% of work in 8 days and another person y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?
P works thrice as fast as Q, whereas P and Q together can work four times as fast as R. If P, Q and R together work on a job, in what ratio should they share the earnings?
There are three pillars X, Y and Z of different heights. Three spiders A, B and C start to climb on these pillars simultaneously. In one chance, A climbs on X by 6 cm but slips down 1 cm. B climbs on Y by 7 cm but slips down 3 cm. C climbs on Z by 6.5 cm but slips down 2 cm. If each of them requires 40 chances to reach the top of the pillars, what is the height of the shortest pillar?
There is an order of 19000 quantity of a particular product from a customer. The firm produces 1000 quantity of that product per out of which 5% are unfit for sale. In how many days will the order be completed?
Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave then and Shyam works for eight more days to complete the job. How long would Ram take to complete the entire job alone?
