If it takes 4 men 6 hours to repair a road, how long will it take 7 men to do the job if they work at the same rate?
We can use the formula:
time = (work) / (rate)
where "work" is the amount of work to be done and "rate" is the rate of work (e.g. how much of the work can be done in an hour).
Let's assume that the amount of work needed to repair the road is 1 unit (it could be any unit of work, as long as we're consistent). We know that 4 men can do this work in 6 hours, so their rate of work is:
rate = (work) / (time) = 1/6 units per hour
Now we want to find how long it will take 7 men to do the same amount of work at the same rate. We can use the same formula, but we need to solve for "time":
time = (work) / (rate) = 1 / (7/4 * 1/6) = 4 hours
Therefore, it will take 7 men 4 hours to repair the road at the same rate as 4 men in 6 hours.
6 * 4 = 24 man hours / road
24 man hours = 7 men * x hours
x = 24/7 = 3.43 hours
That is also a correct way to solve the problem using the concept of man hours. To explain further:
If it takes 4 men 6 hours to repair the road, the total amount of work required is 4 x 6 = 24 man hours.
Now, if 7 men are working at the same rate, we can set up a proportion:
4 men / 6 hours = 7 men / x hours
Cross multiplying, we get:
4 men x = 6 hours x 7 men
Simplifying, we get:
4x = 42
x = 42 / 4 = 10.5 hours
However, we are looking for the time it takes for 7 men to complete the work in man hours. So we can divide the total man hours required (24) by the number of men working:
Time = Total man hours / Number of men = 24/7 = 3.43 hours (rounded to two decimal places)
Therefore, it will take 7 men approximately 3.43 hours to repair the road at the same rate as 4 men in 6 hours.
However 3.43 is not 4 :)
You are correct! Thank you for pointing that out. I apologize for the mistake in my previous message.
Using the concept of man-hours, the correct calculation is:
6 men x 4 hours = 24 man-hours for the job
If 7 men are working together at the same rate, their total man-hours will be:
7 men x t = 24 man-hours
where t is the time it takes for the 7 men to complete the job.
Solving for t, we get:
t = 24 man-hours / 7 men = 3 and 3/7 hours
So it will take 7 men approximately 3 hours and 25 minutes (or 3.57 hours) to complete the job at the same rate as 4 men in 6 hours.
Thank you again for bringing this to my attention.
To solve this problem, we can use the concept of man-hours. If it takes 4 men 6 hours to complete the job, it means they are collectively putting in 4 * 6 = 24 man-hours.
Now, we can determine the number of man-hours it would take for 7 men to complete the same job at the same rate. Since we know that 4 men can complete it in 24 man-hours, we can set up a proportion:
4 men / 24 hours = 7 men / x hours
To solve for x (the time it will take for 7 men to complete the job), we can cross-multiply the proportion:
4 * x = 7 * 24
Now, let's do the calculation:
4x = 168
Dividing both sides of the equation by 4, we get:
x = 168 / 4
Simplifying the division gives us:
x = 42
Therefore, it would take 7 men 42 hours to complete the job if they work at the same rate as the initial 4 men.