Question 10:
Diagram below shows the distance from Town P to Town Q and Town Q to Town R.
(a) Rahim rode his bicycle from Town P at 9.00 a.m. and took 2 hours to reach Town Q.
What is the speed, in km/h, of the bicycle?
(b) Rahim took 30 minutes rest at Town Q and continued his journey to Town R three times faster than his earlier speed.
State the time he reached Town R.

Solution:
(a)
$\begin{array}{l}\text{The speed of the bicycle from Town }P\text{ to Town }Q\\ =\frac{\text{Distance}}{\text{Time}}\\ =\frac{10}{2}\\ =5\text{ km/h}\end{array}$

(b)
$\begin{array}{l}\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\ \\ \text{Rahim took 30 minutes rest at Town }Q\text{.}\\ \text{Time taken when his journey to Town }R\text{ three times}\\ \text{faster than his earlier speed}\text{.}\\ =\frac{25}{5\times 3}\\ =\frac{5}{3}\\ =1\frac{2}{3}\text{ hours}\\ =1\text{ hour 40 minutes }\leftarrow \boxed{\begin{array}{l}\frac{2}{3}\times 60\\ =40\text{ minutes}\end{array}}\\ \\ \text{Total time taken from Town }P\text{ to Town }Q\text{ and Town }Q\text{ to Town }R\\ =2\text{ hours }+30\text{ minutes}+1\text{ hour 40 minutes}\\ =4\text{ hour 10 minutes}\\ \\ \text{The time he reached Town }R\text{ at 1}\text{.10 p}\text{.m}\text{.}\end{array}$

Question 11:
Diagram below shows a trailer travelling from a factory to location P and location P to location Q. The trailer departs at 8.00 a.m.




(a) Based on the Table, calculate the total mass, in tonne, of the trailer and its load.
(b) The trailer arrived at location P at 10.00 a.m. and it stopped for 1½ hours to unload half of the concrete pipes. The trailer then continued its journey to location Q two times faster than its earlier speed. State the time, the trailer reached at location Q.

Solution:
(a)
$\begin{array}{l}\text{Mass of concrete pipe on the trailer}\\ =500\text{ kg}\times 8\\ =4000\text{ kg}\\ =\frac{4000}{1000}\\ =4\text{ tonnes}\\ \\ \text{Total mass of the trailer and its load}\\ =1.5+4.0\\ =5.5\text{ tonnes}\end{array}$

(b)
$\begin{array}{l}\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\ \\ \text{Time taken to travel from the Factory to Location }P\\ =10.00\text{ a}\text{.m}\text{.}-8.00\text{ a}\text{.m}\text{.}\\ =2\text{ hours}\\ \\ \text{Speed of the trailer}\\ =\frac{80}{2}\\ =40\text{ km/h}\\ \\ \text{It stopped for }1\frac{1}{2}\text{ hours to unload half of the concrete pipes}\text{.}\\ \\ \text{Time taken to continue its journey to Location }Q\\ =\frac{\text{Distance}}{\text{Speed}}\\ =\frac{200}{40\times 2}\\ =2\frac{1}{2}\text{ hours}\\ \\ \text{The time the trailer reached at Location }Q\\ =1400\text{ hours or }2.00\text{ p}\text{.m}\text{.}\end{array}$

Question 12:
Diagram below shows travel information of Jason and Mary from Town A to Town B. Jason drives a lorry while Mary drives a car.

(a) Jason started his journey from Town A at 7.00 a.m.
State the time, Jason reached at Town B.
(b) If both of them reached Town B at the same time, state the time Mary started her journey from Town A.

Solution:
(a)
Total time taken from Town A to Town B
= 3 hours + 1 hour + 2 hours
= 6 hours

Time Jason reached Town B
= 0700 + 0600
= 1300 hours → 1.00 p.m.

(b)
$\begin{array}{l}\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\ \text{Total distance from Town }A\text{ to Town }B\\ =\left(60\times 3\right)+\left(75\times 2\right)\\ =180+150\\ =330\text{ km}\\ \\ \text{Time taken by Mary}\\ =\frac{330}{100}\\ =3.3\text{ hours}\\ =3\text{ hours }18\text{ minutes }\leftarrow \boxed{\begin{array}{l}0.3\times 60\\ =18\text{ minutes}\end{array}}\\ \\ \text{The time Mary started her journey from Town }A=9.42\text{ a}\text{.m}\text{.}\end{array}$

Question 6:
Mei Ling drives her car from Kuantan to Kuala Terengganu for a distance of 170 km for 2 hours. She then continues her journey to Kota Bahru and increases her speed to 100 kmh^-1 for 45 minutes.
Calculate the acceleration, in kmh^-2, of the car.

Solution:
$\begin{array}{l}\text{Speed from Kuantan to Kuala Terengganu}\\ =\frac{170}{2}=85{\text{ kmh}}^{-1}\\ \\ \text{Acceleration}\\ =\frac{\text{Final speed}-\text{Initial speed}}{\text{Time taken}}\\ =\frac{100-85}{\frac{45}{60}}\\ =20{\text{ kmh}}^{-2}\end{array}$

Question 7:
Diagram shows the distance between K and L.

A car moves from K to L with an average speed of 80 kmh^-1. After rest for 1 hour 30 minutes, the car then returns to K. The average speed of the car from L to K increases 20%. If the car reaches K at 5 p.m., calculate the time the car starts its journey from K.

Solution: 
$\begin{array}{l}\text{The time taken from }K\text{ to }L\\ =\frac{160}{80}\\ =2\text{ hrs}\\ \\ \text{The average speed from }L\text{ to }K\\ =80\times 1.2\\ =96{\text{ kmh}}^{-1}\\ \\ \text{The time taken from }L\text{ to }K\\ =\frac{160}{96}\\ =1\frac{2}{3}\text{ hrs}\\ \\ \text{The total time taken for the whole journey}\\ =2+1\frac{1}{2}+1\frac{2}{3}\\ =5\frac{1}{6}\text{ hrs}\\ =5\text{ hour }10\text{ minutes}\end{array}$



The car starts its journey from K at 11:50 a.m.

Question 8:
Mr Wong is going to watch a movie at 2.30 p.m at a cinema that is 60 km away from his house. He leaves at 1.25 p.m and drives at an average speed of 70 km/h for half an hour. If he drives at an average speed of 75 km/h for the remaining journey, will he arrive before the movie starts?
Give your reason with calculation.

Solution: 
$\begin{array}{l}\text{Distance travelled at the first }\frac{1}{2}\text{ hour}\\ =70\times \frac{1}{2}\\ =35\text{ km}\\ \\ \text{Remaining distance}=60\text{ km}-35\text{ km}\\ =25\text{ km}\\ \text{Time taken for the remaining journey}\\ =\frac{25}{75}\\ =\frac{1}{3}\times 60\\ =20\text{ minutes}\\ \\ \text{Mr Wong arrives at}\\ =1.25\text{ p}\text{.m}+30\text{ minutes}+20\text{ minutes}\\ =2.15\text{ p}\text{.m}\\ \\ \text{Yes, he will arrive before 2}\text{.30 p}\text{.m}\\ \end{array}$

Question 9:
Karen drives her car from town P to town Q at an average speed of 80 km/h for 2 hours 15 minutes. She continues her journey for a distance of 90 km from town Q to town R and takes 45 minutes.
Calculate the average speed, in km/h, for the journey from P to R.

Solution:
$\begin{array}{l}\text{From }P\text{ to }Q\text{:}\\ \text{Average speed}=80\text{ km/h}\\ \text{Time taken = 2 hours 15 minutes}\\ \text{ = 2}\frac{1}{4}\text{ hours}\\ \text{Distance}=\text{average speed}\times \text{time taken}\\ \text{Distance }=80\times 2\frac{1}{4}\\ =80\times \frac{9}{4}\\ =180\text{ km}\\ \\ \text{From }Q\text{ to }R\text{:}\\ \text{Distance }=90\text{ km}\\ \text{Time taken = 45 minutes}\\ \text{ = }\frac{3}{4}\text{ hour}\\ \\ \text{Average speed from }P\text{ to }R\\ =\frac{180+90}{2\frac{1}{4}+\frac{3}{4}}\leftarrow \boxed{\frac{\text{Total distance}}{\text{Total time}}}\\ =\frac{270}{3}\\ =90\text{ km/h}\end{array}$

Question 1:
The distance from town A to town B is 120 km. A car leaves town A for town B at 11.00 a.m. The average speed is 80 km h^-1 .
At what time does the car arrive at town B.

Solution:
$\begin{array}{l}\text{Time taken}=\frac{\text{distance travelled}}{\text{average speed}}\\ =\frac{120\text{ km}}{80{\text{ km h}}^{-1}}\\ =\frac{3}{2}\text{ hours}\\ \text{= 1 hour 30 minutes}\\ \text{1 hour 30 minutes after 11}\text{.00 a}\text{.m}\text{. is 12}\text{.30 p}\text{.m}\text{.}\end{array}$

Question 2:
Kenny drives his car from town P to town Q at a distance of 180 km in 3 hours.
Faisal takes 30 minutes less than Kenny for the same journey.
Calculate the average speed, in km/h, of Faisal’s car.

Solution:
$\begin{array}{l}\text{Time taken by Faisal}\\ \text{= 3 hours}-30\text{ minutes}\\ \text{= 3 hours}-\frac{1}{2}\text{ hour}\\ \text{= 2}\frac{1}{2}\text{ hours}\\ \\ \text{Average speed of Faisal's car}\\ =\frac{\text{distance travelled}}{\text{time taken}}\\ =\frac{180\text{ km}}{\text{2}\frac{1}{2}\text{ hours}}\\ =72\text{ km/h}\end{array}$

Question 3:
Rafidah drives her car from town L to town M at an average speed of 90 km/h for 2 hours 40 minutes. She continues her journey for a distance of 100 km from town M to town N and takes 1 hour 20 minutes.
Calculate the average speed, in km/h, for the journey from L to M.

Solution:
$\begin{array}{l}\text{Distance}=\text{average speed}\times \text{time taken}\\ \text{Distance from }L\text{ to }M=90\times 2\frac{40}{60}\\ =90\times 2\frac{2}{3}\\ =90\times \frac{8}{3}\\ =240\text{ km}\\ \\ \text{Total distance from }L\text{ to }N=240+100\\ =340\text{ km}\\ \\ \text{Total time taken = 2 hours 40 minutes + 1 hour 20 minutes}\\ \text{ = 4 hours}\\ \text{Average speed for the journey from }L\text{ to }N=\frac{340\text{ km}}{4\text{ h}}\\ =85\text{ km/h}\end{array}$

Question 4:
Susan drives at an average speed of 105 km/h from town F to town G.
The journey takes 3 hours.
Susan takes 30 minutes longer for her return journey from town G to town F. Calculate the average speed, in km/h, for the return journey.

Solution:
$\begin{array}{l}\text{Distance from }F\text{ to }G\\ \text{= 105 km/h}\times \text{3 hours}\\ \text{=315 km}\\ \\ \text{Average speed for return journey}\\ =\frac{\text{distance travelled}}{\text{time taken}}\\ =\frac{315\text{ km}}{3\frac{1}{2}\text{ hours}}\\ =90\text{ km/h}\end{array}$

Question 5:
Table below shows the distances travelled and the average speeds for four vehicles.

Vehicle	Distance (km)	Average speed (km/h)
A	230	115
B	250	100
C	170	85
D	245	70

Which vehicles took the same time to complete the journey?

Solution:
$\begin{array}{l}\text{Time taken for vehicle }A=\frac{230}{115}=2\text{ hours}\\ \text{Time taken for vehicle }B=\frac{250}{100}=2\frac{1}{2}\text{ hours}\\ \text{Time taken for vehicle }C=\frac{170}{85}=2\text{ hours}\\ \text{Time taken for vehicle }D=\frac{245}{60}=3\frac{1}{2}\text{ hours}\end{array}$

Thus, the vehicles A and C took the same time to complete the journey.