Xavier started a work and left after working on it for 4 days. Pakalu completed the remaining work in 18 days. Had Xavier worked for 6 days, Pakalu could have completed the remaining work in next 12 days. If both of them were asked to work on a similar kind of 'work', in how many days can they together complete the work?
Question
Xavier started a work and left after working on it for 4 days. Pakalu completed the remaining work in 18 days. Had Xavier worked for 6 days, Pakalu could have completed the remaining work in next 12 days. If both of them were asked to work on a similar kind of 'work', in how many days can they together complete the work?
Solution
To solve this problem, we first need to understand the concept of work and efficiency in time and work problems.
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Xavier works for 4 days and Pakalu completes the remaining work in 18 days. This means the total work is equivalent to 4 days of Xavier's work + 18 days of Pakalu's work.
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In the second scenario, Xavier works for 6 days and Pakalu completes the remaining work in 12 days. This means the total work is also equivalent to 6 days of Xavier's work + 12 days of Pakalu's work.
Since the total work is the same in both scenarios, we can set these two equations equal to each other:
4X + 18P = 6X + 12P
Solving this equation for X (Xavier's work rate), we get:
X = 2P
This means Xavier's work rate is twice as fast as Pakalu's.
- Now, let's find the time it takes for them to complete the work together. We know that Xavier's work rate is twice as fast as Pakalu's, so let's denote Xavier's work rate as 2x and Pakalu's work rate as x.
The total work can be represented as 4 days of Xavier's work + 18 days of Pakalu's work, or 4(2x) + 18x = 26x.
If they work together, their combined work rate is 2x + x = 3x.
So, the time it takes for them to complete the work together is the total work divided by their combined work rate, or 26x / 3x = 26/3 ≈ 8.67 days.
Therefore, Xavier and Pakalu can together complete the work in approximately 8.67 days.
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