20. (6 points) In the forest, there is a pair of rabbit brothers racing. The younger brother starts running 10 steps ahead, and then the older brother starts chasing. If the younger brother runs 4 steps in the same time the older brother runs 3 steps, and the older brother runs 5 steps for the same distance the younger brother runs 7 steps, then the older brother needs to run $\qquad$ steps to catch up with the younger brother.
【Analysis】Assuming the older brother runs 3 steps in 1 second, then the younger brother runs 4 steps in 1 second;
Since the older brother runs 5 steps equal to the younger brother's 7 steps, the distance the older brother runs in 5 steps must be a multiple of 5 and also a multiple of 7;

Assuming the younger brother runs 5 meters per step, and the older brother runs 7 meters per step, we can then derive the speeds of the older and younger brother, and use the speed difference and distance difference to find the time it takes for the older brother to catch up to the younger brother, and finally determine how many steps the older brother needs to run to catch up to the younger brother.

【Solution】Solution: Assuming the older brother runs 3 steps in 1 second, then the younger brother runs 4 steps in 1 second;
(1) Speed of the younger brother and the older brother:

Speed of the younger brother: $4 \times 5=20$ (meters/second);
Speed of the older brother: $3 \times 7=21$ (meters/second).
(2) Time for the older brother to catch up to the younger brother:
$$
\begin{array}{l}
5 \times 10 \div(21-20), \\
=50 \div 1, \\
=50 \text { (seconds). }
\end{array}
$$
(3) Steps the older brother needs to run to catch up to the younger brother:
$$
50 \times 21 \div 7=150 \text { (steps). }
$$

Answer: The older brother needs to run 150 steps to catch up to the younger brother.
The answer is: 150.