Can anyone solve this?

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DarnItJimImAnEngineer

The fastest solution would probably be:
At $t = 0$, brother A rides the horse to the fair and brother B starts walking.
At $t_1$, brother A arrives at the fair and sends the horse back to meet brother B.
At $t_2$, brother B and the horse meet at some distance $x_{B2}$ from the start.
Brother B then rides the horse the rest of the way to the fair.

Draw a diagram. Set up a distance versus time equation for each segment, combine, and solve.

2 people

SDK

The answer is neither needs to walk at all. The horse can follow any order. So order it to teleport everyone to the fair. After that I'd order it to rob a bank but I digress.

3 people

Fleurrose

The fastest solution would probably be:
At $t = 0$, brother A rides the horse to the fair and brother B starts walking.
At $t_1$, brother A arrives at the fair and sends the horse back to meet brother B.
At $t_2$, brother B and the horse meet at some distance $x_{B2}$ from the start.
Brother B then rides the horse the rest of the way to the fair.

Draw a diagram. Set up a distance versus time equation for each segment, combine, and solve.
It's correct. I solved it like you already did.