Inverse variation

Question

The time, t (in minutes), you need to type a term paper varies inversely with the rate, r (in words per minute), that you can type. When typing 50 words per minute, you can finish in 80 minutes. How long would it take if you could only type 40 words per minute?

Answer 1

Let write a proportion that describes this relationship.

 

r ∝ 1 / t

 

 

We can establish an equation using this proportion:

 

r = K / t

 

where K is a constant.

 

Solve for K using the initial values.

 

K = rt

K = 50 words/min * 80 min

K = 4000 words

 

 

Now, solve for t using the value of K when the rate, r, is 40 words/min.

 

t = K / r

 

t = (4000 words) / (40 words/min)

t = 160,000 min