If it takes five men six hours to dig seven holes, how long does it take one man to dig half a hole?
To solve this problem, we can use the concept of rates. We know that five men can dig seven holes in six hours. Let's break it down step by step to find the rate at which one man can dig a hole.
1. Identify the given information:
- Number of men: 5
- Time taken: 6 hours
- Number of holes dug: 7
2. Find the rate at which the group of five men digs:
- Rate = Number of holes / Time
- Rate of five men = 7 holes / 6 hours
3. Calculate the rate at which one man can dig:
- Divide the rate of five men by 5 (since there are five men):
- Rate of one man = (7 holes / 6 hours) / 5 men
4. Calculate the time it takes for one man to dig half a hole:
- Time = Number of holes / Rate
- Time for one man to dig half a hole = (1/2) hole / (Rate of one man)
Now let's calculate:
Rate of five men = 7 holes / 6 hours = 7/6 holes per hour
Rate of one man = (7/6 holes per hour) / 5 men = 7/30 holes per hour
Time for one man to dig half a hole = (1/2) hole / (7/30 holes per hour)
Time for one man to dig half a hole = (1/2) * (30/7) hours
Simplifying the expression:
Time for one man to dig half a hole = 15/7 hours or approximately 2.14 hours.
Therefore, it would take one man approximately 2.14 hours to dig half a hole.
one man takes (6hr/7holes)5 men = 30/7
man hr per hole
so
15/7 for half a hole