44) a) A bus is travelling at a uniform speed of 50 km/hr. Draw the distance-time graph and hence find (i) the constant of variation (ii) how far will it travel in \(1\frac{1}{2}\) hr (iii) the time required to cover a distance of 300 km from the graph.
Answer:
Let x be the time taken in minutes and y be the distance travelled in km.
| Time taken x (in minutes) | 60 | 120 | 180 | 240 |
|---|---|---|---|---|
| Distance y (in km) | 50 | 100 | 150 | 200 |
(i) Observe that as time increases, the distance travelled also increases. Therefore, the variation is a direct variation. It is of the form y = kx.
Constant of variation:
\(k = \frac{y}{x} = \frac{50}{60} = \frac{100}{120} = \frac{150}{180} = \frac{200}{240} = \frac{5}{6}\)
Hence, the relation may be given as \(y = \frac{5}{6}x\).
(ii) From the graph, if x = 90 minutes (\(1\frac{1}{2}\) hours), then \(y = \frac{5}{6} \times 90 = 75\) km. The distance travelled is 75 km.
(iii) From the graph, if y = 300 km, then \(300 = \frac{5}{6}x \implies x = \frac{300 \times 6}{5} = 360\) minutes (or) 6 hours. The time taken to cover 300 km is 6 hours.
(OR)