Interpretation 83015

A cargo boat with a total weight of 4,500t sailed from the river to the sea. Calculate by how many tons it is possible to increase the weight of the cargo on the boat at sea so that the draft remains the same as in the river. The density of river water is 998 kg/m³. The density of seawater is 1031 kg/m³.

An example of interpretation is buoyancy.

Correct answer:

x =  148.8 t

Step-by-step explanation:

$$\begin{gathered} m_1=4500\text{t}\to \text{kg}=4500\cdot 1000\text{kg}=4500000\text{kg} \\ {\rho }_1=998{\text{kg/m}}^3 \\ {\rho }_2=1031{\text{kg/m}}^3 \\ {m}_1={\rho }_1\cdot V_1 \\ V=m_1/{\rho }_1=4500000/998\doteq 4509.018{\text{m}}^3 \\ {m}_2={\rho }_2\cdot V=1031\cdot 4509.018\doteq 4648797.5952\text{kg} \\ X=m_2-m_1=4648797.5952-4500000\doteq 148797.5952\text{kg} \\ x=X\to \text{t}=X:1000\text{t}=148797.5952:1000\text{t}=148.8\text{t}=148.8\text{t} \end{gathered}$$

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