Math question

Question

it is math word problem on combined variation

 

Suppose that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers. Suppose also that it takes
100
workers
6
weeks to build
4
miles of highway. How many workers would be needed to build
16
miles of highway in
15
weeks?

Answer 1

The first sentence gives you the formula: T = k•L/w  where k is the constant of proportionality, L is the length of highway, w is # of workers.

 

The next part of the problem statement gives you an instance of values of w, T and L; substitute them to find the value of k.

 

Finally, the problem tells you L=16, T=15, and now (knowing k) you can calculate w, to get the desired answer.

 

Almost all Variation problems are of this nature:

1.  formula described

2.  data given enabling discovery of k

3.  evaluation for another specific case.