Question

The time is takes to build a skyscraper is proportional to its height and inversely proportional to the number of construction workers. If it takes 10 workers 2.5 years to build a 20 story building, how long will it take 80 workers to build a 60 story building?

Answer 1

Answer: about 1 year

Step-by-step explanation:

Given : The time is takes to build a skyscraper is proportional to its height and inversely proportional to the number of construction workers.

Let T be the time and N be the number of works and H be the height.

Then, $\dfrac{T_1 N_1}{H_1}=\dfrac{T_2N_2}{H_2}$

Substitute the values , $N_1=10,\ T_1=2.5,\ H_1=20$ and $N_2=80,\ H_2=60$ , we get

$\dfrac{2.5\times10}{20}=\dfrac{T_2\times80}{60}\\\\\Rightarrow\ T_2=\dfrac{2.5\times10\times60 }{20\times80}=0.9375\approx1 \ year$

Hence, it will take about 1 year for 80 workers to build a 60 story building .