Question

a construction team gives an estimate of three months to repave a large stretch of a very busy road with their core crew of 15 people. the government responds that it is too much of an inconvenience to have this busy road obstructed for three months, so the job must be completed in one month.
if the relationship between construction time and crew members is inversely proportional, how many crew members does the construction team need if they are to complete the job in one month?
express your answer as an integer.
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Explanation:

Step1: Define inverse proportionality

Let \(t\) = time (months), \(n\) = number of crew. Inverse proportion: \(t = \frac{k}{n}\), where \(k\) is constant.

Step2: Solve for constant \(k\)

Substitute \(t=3\), \(n=15\):
\(3 = \frac{k}{15}\)
\(k = 3 \times 15 = 45\)

Step3: Find crew for \(t=1\)

Substitute \(t=1\), \(k=45\) into \(t = \frac{k}{n}\):
\(1 = \frac{45}{n}\)
\(n = 45\)

Answer:

45 people