10. (12 points) Optimus Prime, in robot form, departs from location $A$ to location $B$, and can arrive on time; if he transforms into a car from the beginning, his speed increases by $\frac{1}{4}$, and he can arrive 1 hour earlier; if he travels 150 kilometers in robot form, then transforms into a car, with his speed increasing by $\frac{1}{5}$, he can arrive 40 minutes earlier. Therefore, the distance between $A$ and $B$ is. kilometers.
750
【Solution】According to the problem, we have:
If the speed is increased by $\frac{1}{4}$, the ratio of the original speed to the new speed is $1:\left(1+\frac{1}{4}\right)=4: 5$.
The ratio of time is inversely proportional to the speed, which is $5: 4$. The time saved is 1 hour, $1 \div(5-4)=1$ hour, so the original time was 5 hours, and the new time is 4 hours.
If the speed is increased by $\frac{1}{5}$, the ratio of the original speed to the new speed is $1:\left(1+\frac{1}{5}\right)=5: 6$. The time ratio is inversely proportional, which is 6: 5. The time saved is 40 minutes, which is $\frac{2}{3}$ hours, $\frac{2}{3} \div(6-5)=\frac{2}{3}$, so the original time was $\frac{2}{3} \times 6=4$ hours.
Compared to the previous 5 hours, there is a difference of 1 hour, which means 150 kilometers were covered in 1 hour. Therefore, the distance covered in 5 hours is 150 $\times 5=750$ kilometers.

The answer is: 750.