The map below shows the driving distances from Singapore to different parts of Malaysia.
Adapted from https://www.tourradar.com/t/218274
Jonathan drove from Singapore to Kuala Lumpur and then returned from Kuala Lumpur to Singapore during the June holidays. Some details of his average speed are shown below.
| Journey | Average Speed |
|---|
| Singapore to Kuala Lumpur | \(x\text{ km/h}\) |
| Kuala Lumpur to Singapore | \(10\text{ km/h}\) more than the journey from Singapore to Kuala Lumpur |
Write down, in terms of \(x\), the time taken for the journey from Singapore to Kuala Lumpur.[1]
Given that the difference in time taken for the two journeys was 24 minutes, form an equation in \(x\) and show that it reduces to \(x^2+10x-9000=0\).[3]
Solve the equation \(x^2+10x-9000=0\) and find the average speed for the journey from Singapore to Kuala Lumpur.[2]
Jonathan set off at 9:45 pm on Tuesday for his return journey from Kuala Lumpur to Singapore. Find the day and time he reached home, give your answer correct to the nearest minute.[3]
The speed limit and penalties for speeding on Singapore expressways are shown below.
SINGAPORE EXPRESSWAY SPEED LIMIT & SPEEDING PENALTIES
| \(90\text{ km/h}\): Most expressways | \(80\text{ km/h}\): Certain stretches with higher risk |
|---|
| PIE, KPE, AYE, SLE, TPE, ECP | Tunnels; sharp bends; roadworks; other hazardous sections |
SPEEDING PENALTIES (EFFECTIVE 1 JAN 2026)
| Exceeding speed limit by | Demerit points | Fine / action (light vehicle) |
|---|
| Up to \(20\text{ km/h}\) | \(6\) points | \(\$200\) |
| \(>20\text{–}\hspace{0.5em}30\text{ km/h}\) | \(8\) points | \(\$300\) |
| \(>30\text{–}\hspace{0.5em}40\text{ km/h}\) | \(12\) points | \(\$400\) |
| \(>40\text{–}\hspace{0.5em}50\text{ km/h}\) | \(18\) points | Court Prosecution |
| \(>50\text{ km/h}\) | \(24\) points | Court Prosecution and possible licence suspension / disqualification |
Always adhere to the speed limit on the electronic signboards and road signs as it may vary along the expressway.
Any speed above the posted limit is an offence. There is no official speed allowance.
IMPORTANT NOTES
Demerit points are accumulated within 12 months.
Accumulating 24 demerit points within 12 months will result in licence suspension.
Demerit points will be reduced within 12 months from the date of the offence, provided no further demerit points are incurred.
Jonathan claims that he did not exceed the speed limit during his return journey. Do you agree with Jonathan’s claim? Justify your answer using the information provided. State the fine and the number of demerit points, if any, that Jonathan would receive.[2]