Using seconds with rtc for less than a minute timer

Jonathanw82:

   if (pumpState >= 57120 && pumpState < 57165){

digitalWrite (pumpPin, LOW);
      Serial.println("Water Pump ON");                               
  }
  else {
    digitalWrite (pumpPin, HIGH);
    Serial.println("Water Pump OFF");
  }

57165 minus 57120 gives 45.
So, you want your pump on for forty-five seconds?

Also, it looks like the times you chose to turn it on and off are, respectively, 15:52:00 and 15:52:45.

By the way, if you want to convert hours to seconds in code, I suggest multiplying by 3600L rather than 3600. The L at the end means "treat this number as a long".