The temperature rose 4 f every 90 minutes before noon and rose 2 f for every 45 minutes after noon are these rates equivalent

Yes, because the afternoon rate is just the morning rate split in half. Instead of checking the temperature every hour and a half, the temperature was checked every 45 minutes. And, the temperature rate was also split in half when the time was split in half. So basically, if the 2 degrees every 45 minutes was multiplied by 2, (both the time and the temperature) or if the 4 degrees every 90 minutes was divided by 2, (once again, both the time and the temperature) then, they would both be either 2 degrees every 45 minutes, or they would both be 4 degrees every 90 minutes.