Problema Solution
Assume that the length of time it takes to do a major construction
project varies inversely with the 0.7 power of the number of workers
on the project. Suppose that 100 workers can construct an office
building in 250 days. Write the particular equation expressing the
time in terms of the number of workers, and use it to predict the
number of workers needed to construct the building in just 180 days.
Answer provided by our tutors
Let
t = time
n = the number of workers
t*n^0.8 = C, where C is constant
t = 250 days for n = 100 workers
250*100^0.8 = C
C = 250*100^0.8
The particular equation expressing the time in terms of the number of workers is:
t*n^0.80 = 250*100^0.8
t = 250(100/n)^0.80
For t = 180 days we have
180 = 250(100/n)^0.80
250(100/n)^0.80 = 180
........
........
n = 151 workers approximately.