13. (15 points) A motorcycle traveling 120 kilometers takes the same time as a car traveling 180 kilometers. In 7 hours, the distance traveled by the motorcycle is 80 kilometers less than the distance traveled by the car in 6 hours. If the motorcycle starts 2 hours earlier, and then the car starts from the same starting point to catch up, how many hours after the car starts can it catch up to the motorcycle?


【Analysis】First, analyze the ratio of the distances traveled by the two vehicles, which is the ratio of their speeds. The time required can be found by dividing the distance difference by the speed difference.
【Solution】Solution: According to the problem:
The speed of the motorcycle: The speed of the car $=120: 180=2: 3$.
The distance for each part is: $80 \div(3 \times 6-2 \times 7)=20$ (km).
The distance the motorcycle travels in 7 hours is: $20 \times 7 \times 2=280$ (km). The speed of the motorcycle is: $280 \div 7=40$ (km/h).

The distance the car travels in 6 hours is: $20 \times 6 \times 3=360$ (km). The speed of the car is: $360 \div 6=60$ (km/h). $40 \times 2 \div(60-40)=4$ (hours)

Answer: The car can catch up with the motorcycle within 4 hours after it starts.