Aisyah has two rectangular fish tanks, X and Y, each with a tap. Tank X has a base 50 cm by 30 cm and a height of 40 cm. It is 15 filled with water. Tank Y has a base 45 cm by 20 cm and a height of 36 cm. It is empty. Both taps are turned on at the same time. Each tap lets water flow into its tank at a rate of 1.8 l/min.
- By how many centimetres does the water level in each tank rise in one minute?
- At one moment, the water in both tanks is at the same height. What is this height?
Need a hint?
Change litres to cm³ first. Then divide the volume of water each minute by the base area of the tank. For (b), think about how much faster the water in tank Y rises.
Worked answer
- (a) 1.8 l = 1.8 × 1000 = 1800 cm³ of water flows in each minute.
- Base area of tank X = 50 × 30 = 1500 cm², so the rise = 1800 ÷ 1500 = 1.2 cm per minute.
- Base area of tank Y = 45 × 20 = 900 cm², so the rise = 1800 ÷ 900 = 2 cm per minute.
- (b) Water height in tank X at first = 15 × 40 = 8 cm. Tank Y starts at 0 cm, so it is 8 cm behind.
- Tank Y gains 2 − 1.2 = 0.8 cm more each minute, so it catches up in 8 ÷ 0.8 = 10 minutes.
- Height of water in tank Y after 10 minutes = 2 × 10 = 20 cm. Check with tank X: 8 + 1.2 × 10 = 20 cm.
The mistake this question tests
Converting units (kg, ℓ, m, cm³)
Many pupils divide 1.8 by the base area without changing litres to cm³. Others find the time (10 minutes) in (b) but forget that the question asks for the height.
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See the answer →Practise PSLE area & volume until the mistakes stop.
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