QUESTION 4 4.1. If 24 litres of water is pumped in 20 seconds, how long will it take to pump 84 litres in minutes and seconds? 4.2. \( \begin{array}{l}\text { The pressure }(P) \text { on a diver under water is directly proportional to } \\ \text { the square of her depth (d) below the surface of the water. The } \\ \text { diver has reached a depth of } 10 \text { metres. To what depth should the } \\ \text { diver go for the pressure to double? }\end{array} \)

4.1. First, find the rate at which water is pumped:   Rate = 24 litres / 20 seconds = 1.2 litres per second. To pump 84 litres, the time needed is:   Time = 84 litres / 1.2 litres per second = 70 seconds. Expressing 70 seconds in minutes and seconds:   70 seconds = 1 minute and 10 seconds. 4.2. The pressure (P) is directly proportional to the square of the depth (d); that is,   P = k × d², where k is the constant of proportionality. At a depth of 10 metres, the pressure is:   P₁ = k × (10)² = 100k. We want the pressure to double, so:   P₂ = 2P₁ = 200k. At the new depth d₂,   P₂ = k × d₂². Setting these equal gives:   k × d₂² = 200k  →  d₂² = 200. Taking the square root:   d₂ = √200 = 10√2 metres (approximately 14.14 metres). Thus, to double the pressure, the diver should go to a depth of 10√2 metres (≈14.1 metres).