Does gross production (P) and biomass (B) mean the same?
Searching for context from what you wrote, I found this which seems to be an original article later introduced to the textbook you are using. I think this other version is more clear; P refers to photosynthesis, which is also gross production of biomass; B/P is the ratio of standing biomass to new photosynthetic product; rate of biomass production seems wrong unless you expand it to "existing biomass relative to rate of biomass production."

In summary, the correct interpretation should be that P is indeed the gross production, but B/P is simply the ratio of biomass to the gross production. If R is the loss of biomass through respiration and R &lt; P, then both B and B/P will increase (i.e., you will accumulate biomass) until P=R. Probably in this process both P and R also increase, but what is important is that B/P is increasing, which means the new biomass isn't as efficient at new photosynthesis (presumably either because light is a limited resource or because more of the biomass is not held in photosynthetic organisms).

P is in units of mass/time; R is in units of mass/time; B is in units of mass. The equation would be dB/dT = P - R, or another way, B(t1) = B(t0) + (P-R) * (t1-t0), where t1 is some time after t0.