word problem

Question

The amount of time varies directly with the length of the section of highway and inversly with the number of students who will help. If 12 students clean up 4 miles of highway the project will take 2 hours. How long would it take 50 students to clean up 40 miles of highway. 

Answer 1

Let T = time

       L = length

      N = number of students

 

Then, T = kL/N, for some constant, k.

 

Since T = 2 when L = 4 and N = 12, we have 2 = k(4)/12

 

2 = (1/3)k   So, k =6

 

Therefore, T = 6L/N

 

When N = 50 and L = 40, T = 6(40)/50 = 4.8 hours