Math Problem Statement
Solution
It looks like you've uploaded a math question involving work and time. I'll analyze the questions step by step for clarity.
For Question 9: A can finish the work in 20 days, and B can finish it in 12 days. B worked for 9 days. The question asks how many days A alone will need to finish the remaining work.
We can break it down like this:
- A's rate of work is of the total work per day.
- B's rate of work is of the total work per day.
- B worked for 9 days, so the work done by B is .
- The remaining work is .
Now, A needs to finish of the work. Since A’s rate of work is , the time A will take is:
For Question 10: A can do the work in 24 days. If B is 60% more efficient than A, we need to find how many days B would take to do the same work.
B's efficiency is 60% more than A’s, meaning B works 1.6 times faster than A. Therefore, if A takes 24 days, B will take:
So, the correct answer to Question 10 is 15 days.
Would you like further explanation on any specific question or concept? Here are some related questions for further practice:
- If A completes a task in 15 days and B completes the same task in 25 days, how long would they take together?
- If A and B finish a task together in 10 days, and A works alone for 4 days, how many more days does B need to finish the work?
- If B is 50% more efficient than A, how much more time does A need to complete the task if they work alone?
- A can complete a task in 18 days, and B can complete it in 12 days. If they work together for 6 days, how much work is left?
- What is the combined rate of work of two workers, A and B, if A completes the task in 20 days and B completes it in 30 days?
Tip: When solving work problems, always find the individual work rates of the workers involved (work per day) and use them to calculate combined work or remaining work.
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Math Problem Analysis
Mathematical Concepts
Work and Time
Rates of Work
Fractions
Formulas
Work Rate = 1 / Time
Remaining Work = Total Work - Work Done
Theorems
Work done = Rate × Time
Suitable Grade Level
Grades 7-9
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