The line graph shows the amount of water in a tank from 1 p.m. to 5 p.m. The tank was 20% filled at 1 p.m. Water flowed into the tank from 1 p.m. to 5 p.m.

  1. (a)

    During which 1-hour interval was the flow into the tank the greatest?

    Ans : (a) ___ to ___

  2. (b)

    At 5 p.m., what fraction of the tank was filled with water?

    Ans : (b) ___

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Worked solution

29(a)

1. Read the volume of water at each hour from the graph

At 1 p.m.: 66 litres
At 2 p.m.: 1212 litres
At 3 p.m.: 2020 litres
At 4 p.m.: 2525 litres
At 5 p.m.: 2828 litres

2. Calculate the flow (increase in volume) for each 1-hour interval

1 p.m. to 2 p.m.: 12−6=612 - 6 = 6 litres
2 p.m. to 3 p.m.: 20−12=820 - 12 = 8 litres
3 p.m. to 4 p.m.: 25−20=525 - 20 = 5 litres
4 p.m. to 5 p.m.: 28−25=328 - 25 = 3 litres

3. Identify the interval with the greatest flow

The greatest increase is 88 litres, which occurred from 2 p.m. to 3 p.m.

Answer

2 p.m. to 3 p.m.

29(b)

1. Find the total capacity of the tank using the data at 1 p.m.

At 1 p.m., the volume of water is 66 litres, which corresponds to 20%20\% of the tank.
20%→6 litres20\% \rightarrow 6 \text{ litres}
100%→6×5=30 litres100\% \rightarrow 6 \times 5 = 30 \text{ litres}
The total capacity of the tank is 3030 litres.

2. Calculate the fraction of the tank filled at 5 p.m.

At 5 p.m., the volume of water is 2828 litres.
Fraction of tank filled = 2830=1415\frac{28}{30} = \frac{14}{15}

Answer

1415\frac{14}{15}

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