A rectangular tank contained some water at first. A tap was then turned on to fill the tank completely with water. The tap was turned off at the end of 48 minutes. The graph below shows the amount of water in the tank at the end of 48 minutes.

  1. (a)

    In a minute, how many litres of water flowed from the tap?

  2. (b)

    How many litres of water overflowed from the tank at the end of 48 minutes?

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Worked solution

7(a)

1. Identify the initial and final volume of water during the filling phase from the graph

From the graph, at t=0t = 0 min, the volume is 2020 L.
The tank is completely filled at t=24t = 24 min, where the volume is 110110 L.

2. Calculate the total volume of water that flowed from the tap

Total volume flowed = 110−20=90110 - 20 = 90 L

3. Calculate the rate of water flow per minute

Rate = 9024=3.75\frac{90}{24} = 3.75 L/min

Answer

3.753.75 litres

7(b)

1. Determine the duration for which the water overflowed

The tank is completely filled at 2424 minutes. The tap was turned off at 4848 minutes.
Time during which water overflowed = 48−24=2448 - 24 = 24 minutes.

2. Calculate the volume of water that overflowed

From the graph, the amount of water that flowed from the tap in the first 2424 minutes is 110−20=90110 - 20 = 90 L.
Since the tap flows at a constant rate, the amount of water that flowed (and overflowed) in the next 2424 minutes is also 9090 L.
Alternatively, using the rate from part (a) (3.753.75 L/min):
Volume overflowed = 3.75×24=903.75 \times 24 = 90 L.

Answer

9090 L

AI analysis — may contain mistakes.

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