2. Having walked $4 / 9$ of the length of the bridge, the traveler noticed that a car was catching up to him, but it had not yet entered the bridge. Then he turned back and met the car at the beginning of the bridge. If he had continued his movement, the car would have caught up with him at the end of the bridge. Find the ratio of the car's speed to the traveler's speed.

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# Solution

From the condition, it follows that the time it takes for the car to approach the bridge is equal to the time it takes for the traveler to walk $4 / 9$ of the bridge. Therefore, if the traveler continues moving, by the time the car reaches the bridge, he will have walked ${ }^{8} / 9$ of the bridge. This means that during the time it takes for the car to cross the bridge, the traveler manages to walk one-ninth of the bridge, so the speed of the car is 9 times greater than the speed of the traveler.

## Answer 9.