The time required to do a job varies inversely as the number of people working. 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)
3.5
To solve this problem, we can set up a proportion using the concept of inverse variation. The proportion can be expressed as:
(time for first group of workers) / (number of first group of workers) = (time for second group of workers) / (number of second group of workers)
In this case, let's denote:
- t₁ = time required for the first group of workers (7 bricklayers) to build the park well
- n₁ = number of workers in the first group (7 bricklayers)
- t₂ = time required for the second group of workers (10 bricklayers) to build the park well
- n₂ = number of workers in the second group (10 bricklayers)
Using the given information, we have:
t₁ = 5 hours
n₁ = 7 bricklayers
We are asked to find t₂, the time it will take for 10 bricklayers to complete the job.
Setting up the proportion:
t₁ / n₁ = t₂ / n₂
Substituting the known values:
5 / 7 = t₂ / 10
To solve for t₂, we can cross-multiply and then divide:
(5 * 10) / 7 = t₂
50 / 7 = t₂
t₂ ≈ 7.1 hours (rounded to 1 decimal place)
Therefore, it will take approximately 7.1 hours for 10 bricklayers to complete the job.