 Math »
 3 men can dig a trench 3 feet deep working for 3 hours a day in 3 days. How deep a trench can 6 men dig working for 6 hours a day for 6 days?
3 men can dig a trench 3 feet deep working for 3 hours a day in 3 days. How deep a trench can 6 men dig working for 6 hours a day for 6 days?
Discover the math behind trench digging efficiency: 3 men, 3 feet deep, 3 hours/day, 3 days. Now, envision double the workforce, time, and effort. What depth can 6 men reach in 6 hours/day, 6 days?
by Maivizhi A
Updated Mar 05, 2024
3 men can dig a trench 3 feet deep working for 3 hours a day in 3 days. How deep a trench can 6 men dig working for 6 hours a day for 6 days?
6 men working for 6 hours a day for 6 days can dig a trench that is 24 feet deep.
To solve this problem, we can use the concept of manhours, which is a measure of the amount of work performed by one person in one hour.
Given that 3 men can dig a trench 3 feet deep working for 3 hours a day in 3 days, we calculate the total manhours used to dig this trench:
Total manhours = 3 men * 3 hours/day * 3 days = 27 manhours
Now, we need to find out how many manhours it would take for 6 men to dig a trench of unknown depth in 6 days, working 6 hours a day:
Total manhours = 6 men * 6 hours/day * 6 days = 216 manhours
Since the total amount of work (measured in manhours) remains constant, we can set up a proportion to find the depth of the trench dug by 6 men:
27 manhours / 3 feet = 216 manhours / x feet
Crossmultiplying:
27x = 3 * 216
27x = 648
Dividing both sides by 27:
x = 648 / 27
x = 24
So, 6 men working for 6 hours a day for 6 days can dig a trench that is 24 feet deep.
Work and Time in Mathematics
Work and time problems in mathematics typically involve calculating the amount of work done by one or more individuals over a certain period of time. These problems often involve rates of work, such as work per unit of time, and they can be solved using basic principles of algebra and arithmetic. Here's a general overview of how to approach work and time problems:

Understanding the Concept: In these problems, "work" generally refers to a task or job to be completed, while "time" refers to the duration it takes to complete that task.

Identify the Variables: In most work and time problems, you'll need to identify variables such as:
W = amount of work (building the wall)
T = time taken (hours)
R = rate of work (walls per hour)
Example: If it takes 8 workers 10 hours to build a wall, how long would it take 4 workers to build the same wall?
Solution:
Given:
 W = amount of work (building the wall)
 T = time taken (hours)
 R = rate of work (walls per hour)
Given that 8 workers can complete the wall in 10 hours, the rate of work R is: R = W/T = 1/10 wall per hour
Now, if we have 4 workers, the total rate of work is: R = 8 * (1/10) = 8/10 = 4/5 wall per hour
To find the time it would take for 4 workers to complete the wall, we rearrange the formula: T = W/R = 1 / (4/5) = 5/4 hours = 1.25 hours
So, it would take 4 workers approximately 1.25 hours to build the same wall.
3 men can dig a trench 3 feet deep working for 3 hours a day in 3 days. How deep a trench can 6 men dig working for 6 hours a day for 6 days  FAQs
1. What is the concept of manhours?
Manhours refer to the amount of work performed by one person in one hour.
2. How do you calculate total manhours?
Total manhours are calculated by multiplying the number of men, hours worked per day, and the number of days.
3. In the given problem, how many total manhours are used by 3 men to dig a trench?
27 manhours are used by 3 men to dig a trench.
Recent Updates
 Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevati...
 Yuto and Lian are at train stations 1,880 kilometers apart. Yuto boards a train heading...
 Aman’s salary is first increased by 25% and then decreased by 20%. The result is the ...
 P and S can complete a piece of work in 20 and 15 days respectively. They worked togeth...
 Each day that a library book is kept past its due date, a $0.30 fee is charged at midni...
 Teri goes shopping for some new clothes and then out to lunch with a friend. She spends...
 Two pipes A and B can fill a tank is 8 minutes and 14 minutes respectively. If both the...
 A and B stand at distinct points of a circular race track of length 135 m. They cycle a...
 The image of a candle flame placed at a distance of 30 cm from a mirror is formed on a ...
 In pea plants, Tall plant height is dominant over short plant height. If there are 200 ...
 A wall of length 10 m was to be built across an open ground. The height of the wall is ...
 A company contracts to paint 3 houses. Mr. Brown can paint a house in 6 days while Mr. ...
 In a forest 20% of Mushrooms are Red, 50% Brown and 30% White. A Red mushroom is poison...
 In a large population, 76% of the households own microwaves. A simple random sample of ...
 A bag contains 8 red marbles, 9 yellow marbles, 7 green marbles. How many additional re...