Subjects algebra

Aidil Journey

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1. **State the problem:** We analyze Encik Aidil's journey from Taiping to Penaga, covering 90 km with a rest stop at Alor Pongsu after 45 km. 2. **Identify values of m and n on Diagram 9:** - Let $m$ represent the distance from Taiping to Alor Pongsu, which is 45 km. - Let $n$ represent the distance from Alor Pongsu to Penaga, which is $90 - 45 = 45$ km. 3. **Calculate the time the car was stationary:** - The car stopped at Alor Pongsu from 8:55 a.m. to 9:10 a.m. - Time stationary $= 9:10 - 8:55 = 15$ minutes $= \frac{15}{60} = 0.25$ hours. 4. **Calculate the total time of the journey:** - Start: 8:10 a.m. - End: 10:05 a.m. - Total time $= 10:05 - 8:10 = 1$ hour 55 minutes $= 1 + \frac{55}{60} = 1.9167$ hours. 5. **Calculate the average speed:** - Average speed $= \frac{\text{total distance}}{\text{total time} - \text{stationary time}}$ - Total distance $= 90$ km - Moving time $= 1.9167 - 0.25 = 1.6667$ hours - Average speed $= \frac{90}{1.6667} = 54$ kmh$^{-1}$. **Final answers:** - (i) $m = 45$, $n = 45$ - (ii) Time stationary $= 0.25$ hours - (iii) Average speed $= 54$ kmh$^{-1}$