If I measure the recession velocities of 2 galaxies and galaxy A has a velocity twice that of galaxy B, how far away is B if A is 200 Mpc away? (Remember that V = H0 x D)

Hubble deduced that the farther the galaxy is, the more redshifted it is in its spectrum, and noted that all galaxies are "moving away from each other with a speed that increases with distance", and enunciated the now called Hubble–Lemaître Law.

This is mathematically expressed as:

[tex]V=H_{o}D[/tex] (1)

Where:

[tex]V[/tex] is the approximate recession velocity of the galaxy

[tex]H_{o}[/tex] is the Hubble constant

[tex]D[/tex] is the distance

Now, we have two galaxies A and B ande we know the following:

Galaxy A has a velocity twice that of galaxy B

[tex]V_{A}=2V_{B}[/tex] (2)

Galaxy A is 200 Mpc away

[tex]D_{A}=200Mpc[/tex] (3)

According to Hubble Law:

[tex]V_{A}=H_{o}D_{A}[/tex] (4)

[tex]V_{A}=H_{o}200Mpc[/tex] (5)

Substituting (2) in (5):

[tex]2V_{B}=H_{o}200Mpc[/tex] (6)

[tex]V_{B}=\frac{H_{o}200Mpc}{2}[/tex] (7)

[tex]V_{B}=H_{o}100Mpc[/tex] (8)

If [tex]V_{B}=H_{o}D_{B}[/tex] (9)

[tex]D_{B}=\frac{V_{B}}{H_{o}}[/tex] (10)

Substituting (8) in (11):

[tex]D_{B}=\frac{H_{o}100Mpc}{H_{o}}[/tex] (11)

Finally:

[tex]D_{B}=100Mpc[/tex]