Final answer:
The correct equation to describe the situation is w = 700 + 30t. To fill a pool with a garden hose, it would take approximately 1333.33 minutes, and if diverting a river, it would be filled almost instantaneously.
Step-by-step explanation:
The student is asking to write an equation that relates the amount of water in the pond, represented by 'w' (in liters), to the number of minutes that water has been added, represented by 't'. Given that the pond starts with 700 liters of water and water is being added at a rate of 30 liters per minute, the correct equation to represent this situation is w = 700 + 30t.
For part (a) of a related question, to estimate the time it would take to fill a private swimming pool with a capacity of 80,000 liters using a garden hose delivering 60 liters per minute, we would set up the calculation: 80,000 L / 60 L/min, which simplifies to approximately 1333.33 minutes, or about 22.22 hours.
For part (b), if we could divert a river flowing at 5000 m³/s, first we convert the flow rate to liters per second by multiplying by 1,000 (since 1 m³ = 1,000 L). That gives us a flow rate of 5,000,000 L/s. Dividing 80,000 L by this flow rate gives a time of 0.016 seconds to fill the pool, which is practically instantaneous.