it takes 8 men 11h40min to complete a task. If 2 out of 8 men leave after working for 1 hour, how long will it take for the remaining 6 men to complete the tast at the same rate?
8 * 11 2/3 = 93 1/3 man-hours
after 8 man-hr, 6 men must complete the remaining 85 1/3 man-hr
85 1/3 / 6 = ?
11h 40min = 700 minutes
So, each man does 1/5600 of the job in a minute
8 men working for 60 minutes complete 8*60/5600 = 3/35 of the job.
The remaining 6 men have to do 32/35 of the job, so it will take 8/6 as long as the full contingent of 8 men. The time is thus
8/6 * 32/35 * 700 = 1280/3 minutes = 7h6'40"
Better go with Scott. I seem to have lost a factor of 2 somewhere. 7 hours is clearly not long enough for a smaller crew to do almost the whole thing.
Thanks Scott and Steve
Yes, I think Scott I understood
and the answer is 14h 13 1/3min
To find out how long it will take for the remaining 6 men to complete the task, we need to determine the work rate of a single man first.
Given that it takes 8 men 11 hours and 40 minutes to complete the task, we can calculate the total work done by these 8 men in the given time.
We convert the time to minutes:
11 hours = 11 * 60 = 660 minutes
40 minutes = 40 minutes
Total time taken by 8 men = 660 + 40 = 700 minutes
Since it takes 8 men to complete the task in 700 minutes, the work rate of a single man can be determined.
Work done by 8 men in 700 minutes = 1 task
Work done by a single man in 700 minutes = 1 task / 8 men = 1/8 task
Now, after working for 1 hour (60 minutes), 2 men leave. We need to calculate how much work is done by these 2 men in 1 hour and subtract it from the work done by the 6 remaining men.
Work done by 2 men in 60 minutes = (1/8) * 60 minutes = 7.5 minutes
Now, we find the remaining work to be completed by the 6 men:
Remaining work = 1 task - (work done by 2 men in 1 hour)
Remaining work = 1 task - (7.5 minutes / 60 minutes) = 1 - 0.125 = 0.875 task
Finally, we can determine how long it will take for the remaining 6 men to complete the remaining task at the same rate.
Time taken by 6 men to complete 0.875 task = (0.875 task) / (6 men * (1/8 task)) = (0.875 * 8) / 6 = 1.1667 hours
Converting the time back to hours and minutes:
1.1667 hours = 1 hour + (0.1667 * 60 minutes) = 1 hour + 9.9996 minutes
Therefore, it will take approximately 1 hour and 10 minutes (or 1 hour and 10 seconds, rounding off) for the remaining 6 men to complete the task at the same rate.