The time it takes to construct a highway varies directly as the length of the road but inversely with the number of workers. If it takes 50 workers and 8 weeks to construct 2 kilometers of highway, how long will it take 80 workers to construct 15 kilometers of highway? Please show complete solution.
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Answers
Given : The time it takes to construct a highway varies directly as the length of the road but inversely with the number of workers.
it takes 50 workers and 8 weeks to construct 2 kilometers of highway,
To Find : how long will it take 80 workers to construct 15 kilometers of highway?
Solution:
time it takes to construct a highway varies directly as the length of the road but inversely with the number of workers.
T ∝ L
T ∝ 1/W
T = time taken
L = length of road
W = number of Worker
=> T ∝ L/W
=> T = kL/W
k is constant of proportionality
it takes 50 workers and 8 weeks to construct 2 kilometers of highway,
=> 8 = k (2)/50
=> k = 200
Hence T = 200L/W
80 workers to construct 15 kilometers of highway
=> T = 200 ( 15)/80
=> T = 37.5
37.5 week taken by 80 workers to construct 15 kilometers of highway
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