b) The following table shows the data about the number of pipes and the time taken to fill the same tank.
| No. of pipes (x) | 2 | 3 | 6 | 9 |
|---|---|---|---|---|
| Time Taken (in min) (y) | 45 | 30 | 15 | 10 |
Draw the graph for the above data and hence (i) find the time taken to fill the tank when five pipes are used (ii) Find the number of pipes when the time is 9 minutes.
Answer:
1. Variation: As the number of pipes (x) increases, the time taken (y) decreases. This is an indirect variation.
2. Equation: The equation is of the form \(xy = k\).
\(k = 2 \times 45 = 90\)
\(k = 3 \times 30 = 90\)
So, the equation is \(xy = 90\).
3. Points: (2, 45), (3, 30), (6, 15), (9, 10)
4. Solution from Graph:
(i) When 5 pipes are used (x=5), from the graph, the time taken (y) is 18 minutes.
Verification: \(5 \times y = 90 \implies y = \frac{90}{5} = 18\)
(ii) When the time is 9 minutes (y=9), from the graph, the number of pipes (x) is 10.
Verification: \(x \times 9 = 90 \implies x = \frac{90}{9} = 10\)