If a job can be done by 10 workers in 5 hours, the work load is 10(5) = 50 man-hours. If 4 workers is doing the job for 6 hours, the work done is 4(6) = 24 man-hours. A remaining of 50 - 24 = 26 man-hours of work still needs to be done.
Problem
Eleven men could finish the job in 15 days. Five men started the job and four men were added at the beginning of the sixth day. How many days will it take them to finish the job?
To solve this problem, we need to calculate the total man-hours required to complete the job and then determine how many man-hours are left after the first 5 days. Once we have that information, we can find out how long it will take to complete the remaining work with the available workforce.
Let's break it down step by step:
Step 1: Calculate the total man-hours required to complete the job.
If 10 workers can complete the job in 5 hours, then the work load is 10 workers x 5 hours = 50 man-hours per worker.
Step 2: Calculate the man-hours completed in the first 5 days.
We are given that 5 men started the job. Assuming they work for 5 days, the total man-hours completed by these 5 men would be:
5 men x 5 days x 24 hours = 120 man-hours
Step 3: Calculate the man-hours completed on the sixth day.
On the sixth day, four more men are added to the team. They work for 1 day, so the total man-hours completed by these 4 men would be:
4 men x 1 day x 24 hours = 96 man-hours
Step 4: Calculate the remaining man-hours.
To find out how many man-hours of work still need to be done, subtract the man-hours completed from the total man-hours required:
Total man-hours required - man-hours completed = 50 man-hours - (120 man-hours + 96 man-hours) = 50 man-hours - 216 man-hours = -166 man-hours
Since the result is negative (-166 man-hours), it means the initial workforce completed more work than required in the first 6 days.
Step 5: Calculate how long it will take to complete the remaining work.
Since there are no remaining man-hours of work to be done (as calculated in Step 4), it means the job is already completed by the sixth day. Therefore, no additional days are required.
So, the answer is, it will take a total of 6 days to finish the job.
To solve this problem, we need to calculate the number of man-hours required to complete the job and then determine how long it will take the men to accomplish this.
Step 1: Calculate the total number of man-hours required to complete the job.
The original job required 10 workers to complete it in 5 hours, so the total man-hours required is 10 * 5 = 50 man-hours.
Step 2: Calculate the man-hours already completed.
Four workers worked for 6 hours, so the man-hours completed is 4 * 6 = 24 man-hours.
Step 3: Calculate the remaining man-hours to be done.
The remaining man-hours can be calculated as the total man-hours required minus the man-hours already completed, which is 50 - 24 = 26 man-hours.
Step 4: Determine the number of men working every day.
There were 5 men working for the first 5 days, and then 4 more men were added on the 6th day. So, a total of 5 + 4 = 9 men were working from the 6th day onwards.
Step 5: Calculate the number of days required to complete the remaining work.
Since 9 men are working, the total man-hours they can complete in a day is 9 * 24 (hours in a day) = 216 man-hours.
To find the number of days required to complete the remaining 26 man-hours of work, we divide the remaining man-hours by the daily man-hours completed by the 9 men:
26 man-hours / 216 man-hours per day = 0.12 day.
Since we cannot have a fraction of a day, we round up to the next whole day, so it will take the 9 men approximately 1 day to complete the remaining 26 man-hours of work.
Therefore, the total number of days required to finish the job is 6 + 1 = 7 days.