This is a pond in the shape of a prism. It is completely full of water Colin uses a pump to empty the pond.
The level goes down by 30 cm in the first 30 minutes.
Work out how many minutes Colin has to wait for
the pond to completely empty.

Kindly check picture to the question below.

150 minutes

Step-by-step explanation:

Volume of prism = height * base area

Height of prism = 1m

Base area = area of a trapezium

Area of trapezium = 0.5(a + b) h

a, b = parallel sides, h= height of trapezium

Area of trapezium = 0.5(1.4+0.6)*2

Area = 0.5(2)*2 = 2m²

Hence,

V of prism = area of trapezium * height of prism

Volume = 2m² * 1m = 2m³

Decrease in water level due to pumping

20cm decrease in 30minutes

(20/100)m in 30 minutes

0.2 m decrease in height of water

Hence, height of water in prism after 30 minutes pumping :

height - 0.2 = 1 - 0.2 = 0.8m

Volume after 30 minutes of pumping :

Base area * new height

2m² * 0.8m = 1.6m³

Decrease in volume over 30 minutes :

(Initial volume - volume after pumping)

2m³ - 1.6m³ = 0.4m³

If ;

0.4m³ = 30 minutes

1.6m³ = x

0.4x = 48

x = 48 / 0.4

x = 120

Hence, it takes 120 minutes for the remaining 1.6m³ to be emptied.

Hence, total wait time :

120 minutes + 30 minutes

= 150 minutes