B observes that galaxies A and C are moving in opposite directions away from her, A with β = - 0.8 and C with β = + 0.6. What are the speeds of galaxies B and C as observed by someone in galaxy

Answer: Speed of galaxy B with respect to galaxy A = 0.8

Speed of galaxy C with respect to galaxy A = 1.4

Explanation:

Let the speed of galaxy A with respect to galaxy B be Vab & it is equal to Va - Vb = - 0.8

Let the speed of galaxy C with respect to galaxy B be Vcb = Vc - Vb = 0.6

Speed of galaxy B with respect to galaxy A = Vba = Vb - Va = - Vab = - (-0.8) = 0.8

Speed of galaxy C with respect to galaxy A = Vca = Vc - Va

But from above, Vc - Vb = 0.6; Vc = 0.6 + Vb

And Va - Vb = - 0.8; Va = - 0.8 + Vb

Vca = Vc - Va = 0.6 + Vb - (-0.8 + Vb) = 0.6 + Vb + 0.8 - Vb = 0.6 + 0.8 = 1.4

(Solved)