The time between seeing lightning and hearing thunder varies directly with the distance away from the lightning. Eduardo counted 10 seconds between seeing lightning and hearing thunder, and he knew that the lightning was 2 miles away. What is the constant of variation for this problem?

Let us call the time as [tex] t [/tex] and the distance as [tex] d [/tex].It is given that the time between seeing lightning and hearing thunder varies directly with the distance away from the lightning.Mathematically, this direct variation is represented as:[tex] t\propto d [/tex]Now, to remove the [tex] \propto [/tex] sign we replace it by an equal to sign (=) and a constant of variation, k. (Please note that this is an important step)Thus, the above equation becomes:[tex] t=k\times d [/tex]In order to find the constant of variation, k, we isolate k by dividing both sides of the above equation by d. Thus, we get:[tex] \therefore k=\frac{t}{d} [/tex]Plugging in the values of t and d given in the question, we get:[tex] k=\frac{10 seconds}{2 miles} =5 [/tex] seconds per mile.Therefore, the constant of variation for this problem is 5 seconds per mile.