Solution:

This is based on utilization of maximum efficiency

point where 800 carrots can be transported using 2.5 return trips, means in 5 one side trips.

       To reach to this point horse will eat 400 carrots in 5 triops. means this point is 80 miles away. 

Now the remaining distance is 320 miles

Next the point where 400 carrots can be transported in 1.5 round trips or 3 one side trips. 

horse will eat 400 carrots to get there in 3 trips,  means 133 miles away. 

now the remaining distance is 320-133= 187 miles and carrots are 401 left. so now horse will further eat 187 carrots.

So the maximum carrots transported will be 401-187 = 214 carrots