You know the time (T) it takes to build a bridge varies directly as the length (L) of the bridge and inversely to the number of workers (W) it takes 120 days to build a 20m bridge with 10 workers

Question

A. Representation

1. Using symbols

2. Using equation

B. What is the constant of variation?

C. How long will it take to build the bridge if 2 workers will be out?

1. If the length of the bridge will be doubled to make it a two-way-wide bridge, how many weeks will 16 workers build the bridge?

2. Will the bridge be ready before the founding anniversary of the city competition to be held 4 months from now?

E. If the mayor of the city wants the 20m bridge to be finished by 2 months, how many workers will be needed? 

Answer 1

T = kL/W

120 = 20k/10

120 = 2k

k = 60 = constant of variation

T = 60L/W

T =60(20)/(10-2) = 120/8 = 15 day if 2 workers are out

double length with 16 workers

T= 60(40)/16 = 150 day

for 30 day months 150 days = 5 months. It won't be ready in 4 months

T = 2 months = 60 days = 60(20)/W

60=1200/W

W =1200/60 = 20

W = 20 workers to finish 20 m in 2 months