Question

The time, t (in minutes), you need to type acertain paper varies inversely with the rate, r(in words per minute), that you can type.When typing 40 words per minute, you canfinish in 50 minutes. Find the constant ofproportionality and write an equationrelating t and r.?]t =

Answer 1

In order to find the constant of proportionality between t and r, as they are inversely proportional, we just need to multiply their values.

When typing 40 words per minute (that is, r = 40), you can finish in 50 minutes (that is, t = 50). So the constant is:

`40\cdot50=2000`

Now, to write an equation relating t and r, we use this variables in the product above, and make their product equal the constant we found. Then, we isolate the variable t:

`\begin{gathered} t\cdot r=2000 \\ t=(2000)/(r) \end{gathered}`