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?

Answer 1

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.

Answer 2

6 * 4 = 24 man hours / road
24 man hours = 7 men * x hours
x = 24/7 = 3.43 hours

Answer 3

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.

Answer 4

However 3.43 is not 4 :)

Answer 5

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.