Nowhere does it say you need to travel at a normal pace after galloping. Galloping for just an hour means you gain the benefits of a full day of fast travel while otherwise travelling at a normal pace (and not suffered the penalty on Perception).

I think that is not correct. The PHB states the following on page 181:

* "Mounts and Vehicles. For short spans of time (up to an hour), many animaIs move much faster than humanoids. A mounted character can ride at a gallop for about an hour, covering twice the usual distance for a fast pace."*
That means:

a) You can only gallop for one hour

b) You gain the benefit of twice the distance of "fast pace" - BUT: You pick that from the table shown on page 182 that states "4 miles". So you can gallop for a total of 8 miles.

I am actually sharing your opinion, Jester David. But I wanted to know what RAW intends.

**Correct me, if I am still wrong. But I think RAW states the following points:**

1.) You do not travel faster while mounted.

2.) You can only gallop for one hour per day (covering twice the usual distance for a fast pace).

3.) There is no need of a rest after galloping. And there is no rule saying you need to continue travelling at "slow" or "normal" pace. A horse simply can't gallop anymore for that day.

4.) If you travel more than 8 hours, the traveler has to make a check for exhaustion - regardless of whether he is riding a mount or walking. (DM might also ask for a check for the mount.)

**EDIT:**
Here is the table of the PHB 182. Remember:

*A mounted character can ride at a gallop for about an hour, covering twice the usual distance for a fast pace."*
**Speed** | **Minute** | **Hour** | **Day** | **Effect** |

Fast | 400 Feet | 4 Miles | 30 Miles | -5 Passive Perception |

Normal | 300 Feet | 3 Miles | 24 Miles | – |

Slow | 200 Feet | 2 Miles | 18 Miles | Stealth possible |