- 9 days
- 6 days
- 5 days
- 8 days
1. Determine the individual work rates:
- Man’s work rate: If he completes the task in 15 days, he completes 151 of the task per day.
- Friend’s work rate: If he completes the task in 10 days, he completes 101 of the task per day.
Explanation: The work rate represents the fraction of the total task that each person can complete in one day.
2. Calculate their combined work rate:
- When they work together, their work rates add up.
- Combined work rate = Man’s work rate + Friend’s work rate
- Combined work rate = 151+101
To add these fractions, find a common denominator (the least common multiple of 15 and 10 is 30):
- 151=15×21×2=302
- 101=10×31×3=303
- Combined work rate = 302+303=302+3=305=61
Explanation: When working together, the fraction of the task they complete each day is the sum of their individual fractions of work completed per day.
3. Calculate the time taken to complete the task together:
- If they complete 61 of the task per day, the total number of days to complete the entire task (which represents 1 whole task) is the reciprocal of their combined work rate.
- Time taken together = 1/Combined work rate
- =1/0.6=6 days.
Explanation: The time taken to complete the entire task is the inverse of the fraction of the task completed per day when working together.
Therefore, if they work together, they will take 6 days to complete the task.