if it takes 5 men 7 days to dig a hole, how long will it takes 3 men to dig half a hole?
3/5 as many men, so 5/3 as long for one hole.
That is, it will take 3 men 7 * 5/3 = 35/3 days to dig a whole hole.
so how long for 1/2 a hole?
7 * 5 = 35 ... man-days to dig hole
half a hole takes 35/2 man-days
(35/2) / 3 = 35/6 man-days for half a hole ... almost six days
To solve this problem, we can use the concept of man-hours.
Given that it takes 5 men 7 days to dig a hole, we can calculate the total man-hours required to complete the task.
Total man-hours = Number of men * Number of days = 5 men * 7 days = 35 man-hours.
Now, we need to find out how long it will take 3 men to dig half a hole, which means we need to calculate half of the total man-hours.
Half of the total man-hours = 1/2 * 35 man-hours = 17.5 man-hours.
To find out how long it will take 3 men to complete 17.5 man-hours of work, we divide the total man-hours by the number of men.
Time taken by 3 men to complete 17.5 man-hours = 17.5 man-hours / 3 men = 5.83 days.
Therefore, it will take approximately 5.83 days for 3 men to dig half a hole.
To solve this problem, we first need to determine the rate at which men can dig holes. We do this by calculating the rate of work for 5 men digging a hole in 7 days.
If 5 men can dig a hole in 7 days, we can assume that 1 man's work for the same length of time is equivalent to 1/5 of the work of 5 men. Therefore, we can say that the rate at which a man can dig a hole is 1/5 of a hole per day.
Now, we can determine how long it will take 3 men to dig half a hole. Since we know the rate per man is 1/5 of a hole per day, for 3 men, the combined rate would be 3 times the individual rate, or 3/5 of a hole per day.
To calculate the time it takes for 3 men to dig half a hole, we can set up a proportion:
(3/5) hole per day = 1/2 hole / x days
To solve for x (the number of days), we can cross-multiply and solve for x:
(3/5) * x = 1/2
To get x by itself, we can multiply both sides by 5/3:
x = (5/3) * (1/2)
x = 5/6
Therefore, it will take 3 men approximately 5/6 of a day (or equivalently, 10 hours) to dig half a hole.