Math Problem Statement
Virat can complete a work in 30 days and Daniel is 60% more efficient than Virat to complete the same work. Find the total time taken by Daniel to complete the work.
Solution
To find how long it will take Daniel to complete the work, let's break down the problem step-by-step:
Step 1: Determine Virat's work rate
- Virat completes the entire work in 30 days.
- Therefore, Virat's rate of work is of the work per day.
Step 2: Determine Daniel's work rate
- Daniel is 60% more efficient than Virat. This means Daniel can do 60% more work in the same amount of time.
- If Virat’s efficiency is 100%, then Daniel’s efficiency is of Virat’s efficiency.
- Thus, Daniel’s work rate is of the work per day.
Step 3: Calculate the total time taken by Daniel
- To find how long it takes Daniel to complete the work, we need to find the reciprocal of Daniel’s work rate.
- Time taken by Daniel = days.
Conclusion:
Daniel will take 18.75 days to complete the work.
Would you like further details or have any questions about the process? Here are 5 related questions to explore this concept:
- How would the time change if Daniel were only 40% more efficient than Virat?
- If Virat and Daniel worked together, how long would it take them to complete the task?
- What if Virat and Daniel alternated days of work—how long would the task take?
- If Daniel’s efficiency increased to 100% more than Virat’s, how long would he take to finish?
- How much of the work would Daniel complete in 10 days?
Tip: Efficiency increases directly reduce the time taken to complete a task, but the relationship is not linear—doubling efficiency halves the time required.
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Math Problem Analysis
Mathematical Concepts
Work and Time
Efficiency
Ratio and Proportion
Formulas
Work Rate = 1 / Time
Efficiency Ratio = 1 + (Percentage Increase / 100)
Time = 1 / Work Rate
Theorems
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Suitable Grade Level
Grades 8-10
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