If 14 men can dig a hole 10 metres long in 6 days, how long would 12 men take to dig a hole 15 metres long?
14 men dig 10 metres in 6 days
1 man digs 10/14 m in 6 days
12 men dig 10/14(12) m in 6 days, or
12 men dig 60/7 m in 6 days
12 men dig 1 metre in 6÷(60/7) day, or
12 men dig 1 metre in 7/10 days
12 men dig 15 metres in (7/10)(15) days
12 men dig 15 metres in 10.5 days
To find the answer, we can use the concept of work. The amount of work done to dig the hole is equal to the length of the hole being dug. So, if we assume that the rate of work is constant, we can set up a proportion to solve the problem.
First, let's determine the total work required to dig a 10-meter long hole. Since 14 men can complete this work in 6 days, we can say that their combined work rate is (10 meters)/(6 days). Using this information, we can calculate their individual work rate.
So, the work rate of one man is given by (10 meters)/(6 days)/(14 men), which simplifies to (10/6)/14 = 5/21. This represents the amount of work that one man does in one day.
Now we can apply this work rate to find out how many days it would take 12 men to dig a 15-meter long hole. The amount of work required for a 15-meter long hole is 15 meters.
The work done by 12 men in one day is (12 men) * (5/21), which simplifies to (60/21) = 20/7.
Therefore, it would take 12 men (15 meters) / (20/7) = (15 * 7) / 20 = 7 * 7 / 4 = 49/4, or approximately 12.25 days, to dig a 15-meter long hole.
So, the answer is that it would take approximately 12.25 days for 12 men to dig a 15-meter long hole.