It takes 5hr for 7 bricklayers to build a park well. How long will it take 10 bricklayers to complete the job? (round answer to 1 decimal place)
We can use the formula:
Time = Work / Rate
where Work is the amount of work to be done (in this case, building a park well) and Rate is the rate of work (in this case, the number of park wells built per hour).
Let's say that building one park well is the "unit of work" and that we need 1 unit of work done.
For 7 bricklayers:
Time = Work / Rate
Time = 1 / (7 park wells / 5 hours)
Time = 1 / (1.4 park wells/hr)
Time = 0.71 hours
For 10 bricklayers:
Time = Work / Rate
Time = 1 / (10 park wells / r hours) where r is the rate of work for 10 bricklayers
Time = r / 10
We know that the amount of work to be done is the same (1 unit), so:
0.71 hours * 7 bricklayers = r * t hours * 10 bricklayers
4.97 = 10r * t
t = 4.97 / 10r
We need to find r.
For 7 bricklayers:
Rate = 7 park wells / 5 hours
Rate = 1.4 park wells/hr
Since we know that the park well takes the same amount of time to build no matter how many bricklayers are working on it, the rate of work for 10 bricklayers should be proportional to the rate for 7 bricklayers:
Rate (10) / Rate (7) = 10 / 7
So:
Rate (10) = Rate (7) * 10 / 7
Rate (10) = 1.4 park wells/hr * 10 / 7
Rate (10) = 2 park wells/hr
Now we can plug in everything we know:
t = 4.97 / (10 * 2)
t = 0.25 hours
Rounded to one decimal place, it would take 0.3 hours or approximately 18 minutes for 10 bricklayers to complete the job.