There are two tanks on a property, Tank `A` and Tank `B`. Initially, Tank `A` holds 1000 litres of water and Tank B is empty.
- Tank `A` begins to lose water at a constant rate of 20 litres per minute. The volume of water in Tank `A` is modelled by `V = 1000 - 20t` where `V` is the volume in litres and `t` is the time in minutes from when the tank begins to lose water. (1 mark)
On the grid below, draw the graph of this model and label it as Tank `A`.
- Tank `B` remains empty until `t=15` when water is added to it at a constant rate of 30 litres per minute.
By drawing a line on the grid (above), or otherwise, find the value of `t` when the two tanks contain the same volume of water. (2 marks)
- Using the graphs drawn, or otherwise, find the value of `t` (where `t > 0`) when the total volume of water in the two tanks is 1000 litres. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- `text{T} text{ank} \ A \ text{will pass trough (0, 1000) and (50, 0)}`
- `29 \ text{minutes}`
- `45 \ text{minutes}`
a. `text{T} text{ank} \ A \ text{will pass trough (0, 1000) and (50, 0)}`
b. `text{T} text{ank} \ B \ text{will pass through (15, 0) and (45, 900)}`
`text{By inspection, the two graphs intersect at} \ \ t = 29 \ text{minutes}`
c. `text{Strategy 1}`
`text{By inspection of the graph, consider} \ \ t = 45`
`text{T} text{ank A} = 100 \ text{L} , \ text{T} text{ank B} =900 \ text{L} `
`:.\ text(Total volume = 1000 L when t = 45)`
`text{Strategy 2}`
| `text{Total Volume}` | `=text{T} text{ank A} + text{T} text{ank B}` |
| `1000` | `= 1000 – 20t + (t – 15) xx 30` |
| `1000` | `= 1000 – 20t + 30t – 450 ` |
| `10t` | `= 450` |
| `t` | `= 45 \ text{minutes}` |
