20. Xiaoming sets off from home to his grandmother's house, cycling at a speed of 12 kilometers per hour. 2.5 hours after he leaves, his father realizes that Xiaoming has forgotten his homework, so he sets off on a motorcycle at a speed of 36 kilometers per hour to catch up. As a result, half an hour after Xiaoming arrives at his grandmother's house, his father also arrives. The distance from Xiaoming's home to his grandmother's house is $\qquad$ kilometers.
【Solution】Solution: Let's assume that Xiaoming's father drove for $x$ hours, we can get the equation:
$$
\begin{aligned}
12 \times(2.5-0.5+x) & =36 x, \\
24+12 x & =36 x, \\
24 x & =24, \\
x & =1 ;
\end{aligned}
$$

Then the distance from Xiaoming's home to his grandmother's home is: $36 \times 1=36$ (km).
Answer: The distance from Xiaoming's home to his grandmother's home is 36 km.
Therefore, the answer is: 36.