Chapter 8: Problem 5
A can do a piece of work in 10 days, \(B\) can do it in 15 days working together they can finish the work in : (a) 9 (b) 8 (c) 10 (d) 6
Short Answer
Expert verified
Answer: 6 days
Step by step solution
01
Understand the problem and determine the given information
A can complete the work in 10 days, and B can complete the work in 15 days. We need to find how many days they would complete the work when working together.
02
Calculate the work done by A and B in one day
To find out the work done by A and B in one day, we will use the formula:
Work Done = Total Work / Time
Work Done by A in one day = \(\frac{1}{10}\)
Work Done by B in one day = \(\frac{1}{15}\)
03
Calculate the work done by A and B together in one day
Now, we will find out how much work A and B can do together in one day. For this, we will add the work done by A and B in one day as they are working together.
Work Done by A and B together in one day = Work Done by A in one day + Work Done by B in one day
Work Done by A and B together in one day = \(\frac{1}{10} + \frac{1}{15}\)
04
Simplify the expression and find out the time it takes for A and B to complete the work together
We need to simplify the expression and find the time it takes for A and B to complete the work together.
Work Done by A and B together in one day = \(\frac{1}{10} + \frac{1}{15} = \frac{3}{30} + \frac{2}{30} = \frac{5}{30} = \frac{1}{6}\)
Now, to find the time it takes for A and B to complete the work together, we can use the formula:
Time = Total Work / Work Done in one day
Time = \(\frac{1}{\frac{1}{6}} = 6\) days
So, when working together, A and B can complete the work in 6 days. The correct answer is (d) 6.
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with Vaia!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Collaborative Work Efficiency
When individuals collaborate on a task, the overall efficiency can significantly improve. Combining efforts allows them to complement each other's strengths, often speeding up the completion of the work.
A common scenario involves two people, A and B, working together to complete a single task. On their own, they have different times to complete the work, but together, they become more efficient. This is called collaborative work efficiency.
In essence, when A and B team up, they combine their individual capabilities for greater effect. This results in a faster completion time compared to when they work separately.
A common scenario involves two people, A and B, working together to complete a single task. On their own, they have different times to complete the work, but together, they become more efficient. This is called collaborative work efficiency.
In essence, when A and B team up, they combine their individual capabilities for greater effect. This results in a faster completion time compared to when they work separately.
Rate of Work
To understand collaborative work efficiency, it is crucial to comprehend each worker's rate of work. This rate is defined as the part of the work that one can complete in a given time frame.
For example, if A can complete the work in 10 days, then A's rate of work is \( \frac{1}{10} \). Similarly, B's rate of work is \( \frac{1}{15} \) because B completes the work in 15 days.
By determining the rate of work for each participant, we lay the groundwork for calculating their combined work rate when they work together. This is a critical step in solving any problem involving collaborative work.
For example, if A can complete the work in 10 days, then A's rate of work is \( \frac{1}{10} \). Similarly, B's rate of work is \( \frac{1}{15} \) because B completes the work in 15 days.
By determining the rate of work for each participant, we lay the groundwork for calculating their combined work rate when they work together. This is a critical step in solving any problem involving collaborative work.
Fractional Work Calculation
Once we know the individual rates of work, calculating how much work A and B can achieve jointly in one day becomes straightforward. Since A's rate is \( \frac{1}{10} \) and B's is \( \frac{1}{15} \), their combined work rate for one day is the sum of these individual rates.
In this scenario, it translates to \( \frac{1}{10} + \frac{1}{15} = \frac{5}{30} = \frac{1}{6} \). This denotes that together, A and B can complete \( \frac{1}{6} \) of the work in one day.
The fractional work calculation is an essential concept as it reveals the proportion of the task completed by the team each day. Knowing this allows us to determine how long it will take for the entire task to be finished when working collaboratively.
In this scenario, it translates to \( \frac{1}{10} + \frac{1}{15} = \frac{5}{30} = \frac{1}{6} \). This denotes that together, A and B can complete \( \frac{1}{6} \) of the work in one day.
The fractional work calculation is an essential concept as it reveals the proportion of the task completed by the team each day. Knowing this allows us to determine how long it will take for the entire task to be finished when working collaboratively.