It takes 3 men to dig 2 identical trenches in 5 hours.If all the men work at same rate,how long will it take 5 men to dig 7 of these trenches?
Hmmmm. This question is very 🤯😨( confusing) so can you tell easy trick to solve all the questions.
To solve this problem, let's break it down into steps:
Step 1: Calculate the rate at which the three men dig one trench.
Since it takes 3 men to dig 2 identical trenches in 5 hours, we can find their rate by dividing the number of trenches by the time it takes:
Rate of 3 men = 2 trenches / 5 hours.
Step 2: Calculate the rate at which each man digs one trench.
Since the three men are working at the same rate, we divide the rate of the three men by 3 to find the rate of each man:
Rate of each man = (2 trenches / 5 hours) / 3 = 2/5/3 = 2/15 trenches per hour.
Step 3: Calculate the time it takes for 5 men to dig one trench.
Since each man can dig 2/15 trenches per hour, the combined rate of 5 men would be:
Rate of 5 men = (2/15 trenches per hour) * 5 men = 2/3 trenches per hour.
Step 4: Calculate the time it takes for 5 men to dig 7 trenches.
To find the time it takes for 5 men to dig 7 trenches, we divide the total number of trenches by the rate of 5 men:
Time = 7 trenches / (2/3 trenches per hour)
Step 5: Simplify the expression to find the solution:
Time = 7 * (3/2) = 21/2 = 10.5 hours.
Therefore, it will take 5 men approximately 10.5 hours to dig 7 identical trenches.
To solve this problem, we can use the concept of man-hours.
Given that 3 men can dig 2 trenches in 5 hours, we can calculate the number of man-hours required to dig one trench. Since it took 3 men a total of 5 hours to dig 2 trenches, that means it took them a total of 3 * 5 = 15 man-hours to dig those 2 trenches.
Now, we need to find how many man-hours it takes to dig one trench. We can do this by dividing the total man-hours (15) by the number of trenches (2). So, each trench requires 15 / 2 = 7.5 man-hours.
Next, we can calculate how long it would take a team of 5 men to dig one trench. If one trench requires 7.5 man-hours, then with 5 men working together, they can complete one trench in 7.5 / 5 = 1.5 hours.
Finally, we need to find how long it would take 5 men to dig 7 trenches. Since it takes them 1.5 hours to dig one trench, it would take them 1.5 * 7 = 10.5 hours to dig 7 trenches.
Therefore, it would take 5 men approximately 10.5 hours to dig 7 of these identical trenches.
2 trenches = 3*5 = 15 man-hr
7 trenches = 7/2 * 15 = 105/2 man-hr
(105/2 man-hr) / (5 man) = 21/2 hr
or, 10 hr 30 min