Unraveling Hubble Law and Integral: A PF Forum Guide

[Stephanus]

Dear PF Forum,
I know this is a very basic, basic question. But I'd like to refresh my memory.
In Hubble Law.
$V = H_0 \, D$
$H_0$ is Hubble constant, aproximately $\frac{1}{3.1E17t}$
Okayy, let's say we alter those number to an easier number.
For every 10 metres, the velocity adds 1 m/s.
This is how we write, ok?
$V = 0.1\, D$
And now this.
If an object 1000 metres from us, speeding 100m/s, of course. What time does it takes to reach 4000 metres from us?
Time is Distance / Speed.
What is the formula?
Is this correct?
$\int_a^b \frac{H_0}{x}dx, a = 1000, b = 4000$

 

[RyanH42]

$V=dx/dt$ then $dt=dx/V$ then integrate it $V=HD$ İnside the integral will be $1/H_0xdx$

 

[Stephanus]

$V=dx/dt$ then $dt=dx/V$ then integrate it $V=HD$ İnside the integral will be $1/H_0dx$

Ahh, of course H₀ is the divider, how careless I am!
Thanks.