Question

the time, t(in minutes), you need to type a certain paper varies inversely with the rate, r(in words per minute), that you can type. when typing 40 words per minute, you can finish in 50 minutes. find the constant of proportionality and write an equation relating t and r

Answer 1

Answer:t=2000/r

Step-by-step explanation: I also use acellus and that is the correct answer. i got this by knowing that k= equals the constant of proportionality. So taking that and the given, i would say 50=k/40. To get rid of the fraction, we multiply both sides by 40.

Answer 2

Equation relating t and r is
`t = 2000 (1)/(r)` and constant of proportionality is 2000

Explanation:

Given : the time, t(in minutes), you need to type a certain paper varies inversely with the rate, r(in words per minute), that you can type.

To Find: When typing 40 words per minute, you can finish in 50 minutes. find the constant of proportionality and write an equation relating t and r

Solution:

we are given that t(in minutes), you need to type a certain paper varies inversely with the rate, r(in words per minute), that you can type.

So,
`t \propto (1)/(r)`

`\Rightarrow t = k (1)/(r)` ---1 Where k is the constant of proportionality

We are given that at r= 40 the value of t is 50

Substitute the values in 1

`\Rightarrow 50 = k (1)/(40)`

`\Rightarrow 50 * 40 = k`

`\Rightarrow 2000 = k`

Substitute the value of k in 1

`\Rightarrow t = 2000 (1)/(r)`

Hence equation relating t and r is
`t = 2000 (1)/(r)` and constant of proportionality is 2000