One. (20 points) A batch of goods is prepared to be transported to a certain place, and there are three trucks, A, B, and C, available for hire. It is known that the cargo capacity of trucks A, B, and C remains constant each time, and trucks A and B would need $2a$ and $a$ trips, respectively, to transport this batch of goods alone. If trucks A and C work together for the same number of trips to transport the goods, truck A will transport a total of $180 \mathrm{t}$. If trucks B and C work together for the same number of trips to transport the goods, truck B will transport a total of 270 t. Now, if trucks A, B, and C work together for the same number of trips to transport the goods, how much should the cargo owner pay each truck owner (calculated at 20 yuan per ton)?
Obviously, the load capacity of vehicle B is twice that of vehicle A.
Let the total weight of this batch of goods be $M \mathrm{t}$, and vehicles A and C together transport the goods in $b$ trips, while vehicles B and C together transport the goods in $c$ trips. Since the load capacity of vehicle C remains unchanged when working with A and B, we have
$$
\frac{M-180}{b}=\frac{M-270}{c} \text {. }
$$

It is also obvious that
$$
\frac{180}{b} \times 2=\frac{270}{c} \text {. }
$$

Solving these equations, we get $\frac{b}{c}=\frac{4}{3}, M=540$.
According to the problem, when vehicles B and C work together, vehicle B transports a total of $270 \mathrm{t}$, so vehicle C also transports $270 \mathrm{t}$, meaning the load capacities of vehicles B and C are equal. Therefore, the load capacities of vehicles A, B, and C are in the ratio $1: 2: 2$. Thus, when the three vehicles work together for the same number of trips to transport the goods, they each transport $108 \mathrm{t}, 216 \mathrm{t}, 216 \mathrm{t}$, and the three vehicle owners should receive 2160 yuan, 4320 yuan, and 4320 yuan, respectively.