Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q15

A car and a van started travelling from Town X to Town Y at the same time. The distance between the two towns was 225 km. Both vehicles did not change their speed. The car arrived at Town Y 3/4 h earlier than the van. When the car reached Town Y, the van was still 45 km away from Town Y. What was the speed which the car was travelling?

Solution

* When the car reached Town Y, the van was still 45 km away. The car arrived at Town Y 3/4 h earlier than the van.

(Van) speed -----
45 km divided by (3/4) h
= 60 km/h

(Van) time for the whole journey -----
225 km divided by 60 km/h = 3 and 3/4 hours

Therefore, the car travelled in 3 h.

Speed of car -----
225 km divided by 3 h = 75 km/h

Answer: 75 km/h

Printer Friendly Version

ACS Primary 2010 SA1 Math Paper 2 Q14

Tony and Charles took part in a car race. Tony drove at a speed of 90km/h. Both of them did not change their speed throughout the race. When Charles had covered 1/3 the distance, Tony was 15 km in front of him. Tony reached the finishing line at 9.35 a.m. At what time did Charles recah the finishing line?

Solution

* For every 1/3 of the race Charles covered, Tony was 15 km ahead. When Charles completed the whole race, Tony would have been 3 x 15km = 45km ahead of Charles, if we assume Tony continued to travel beyond the finishing line.

Time = 45 km divided 90 km/h
= 0.5 hour

Half hour after 9.35 am ------ 10.05 am

Answer: 10.05 am

Printer Friendly Version

Math Problem Sum again

To all,
Posted through email from a reader
Please feel free to put up your working and answer
===================
David and Michael drove from town A to town B at different speeds. Both did not change their speeds throughout their journeys. David started his journey 30 mins earlier thatn micheal. however, micheal reached town B 5o mins earlier than david. when micheal reached town B, david had travelled 4/5 of the journey and was 75 km away from town B.

what was the distance between town a and b?
hown many kilometers did david travel in 1 hour?
what was the time taken by micheal to travel from town a to b?

sry to disturb u again but i really need help cause i dont have tuition at home.
===================

RGS Primary 2009 PSLE Math Prelim Paper 2 Q17

At 9.30 am, Train A which was 200 m long, pulled out of Nanas Station and travelled towards Dadas Station at a uniform speed of 80 km/h. Half an hour later, Train B which was 150 m long, left Dadas Station and travelled towards Nanas Station at a uniform speed of 90 km/h.

a) How far has Train A travelled when Train B left Dadas Station?

b) The two trains met each other in a tunnel. Both trains took 15 minutes to completely travel through the tunnel. Calculate the length of the tunnel.

Solution

a)

Distance = speed x time

= 80 km/h x (1/2) hour

= 40 km

Answer: 40 km

b)

(Train A) distance

= 80 km x (1/4) hr

= 20 km

(Train B) distance

= 90 km x (1/4) hr

= 22.5 km

Length of Tunnel

--> 20km + 22.5km - 0.2km (Train A's length) - 0.15km (Train B's length)

= 42.15 km

Answer: 42.15 km

Printer Friendly Version

ACS Primary 2009 PSLE Math Prelim Paper 2 Q14

At 9.30 am, Mr Yeo left Town A for Town B driving at a speed of 75 km/h throughout his journey. At 10.30 am, Mr Lee also left Town A for Town B driving at a certain speed. He kept to the same speed throughout his journey. At 1.30 pm, both of them passed a Shopping Mall that was 150 km way from Town B. How many minutes earlier did Mr Lee reach Town B than Mr Yeo?

Solution

(Town A to Shopping Mall)

Yeo --> distance = 75 km/h x 4h = 300 km

Lee ---> speed = 300 km divided by 3h = 100 kmh

(Shopping Mall to Town B)

Lee --> time = 150 km divided by 100 km/h = 1.5 h

Yeo --> time = 150 km divided by 75 km/h = 2 h

2 h - 1.5 h

= 0.5 h

= 30 min

Answer: 30 minutes

Printer Friendly Version

Rosyth Sch 2007 PSLE Math Prelim Q48

A bus was travelling at a constant speed from Town A to Town B. It passed a car travelling at a constant speed of 90 km/h in the opposite direction. 1 and 1/2 hours later, the bus reached Town B but the car was still 25 km away from Town A. If the bus took 4 hours to complete the whole journey, what is the distance between the two towns?

Solution



Answer: 256 km

Raffles Girls Pri Sch 2007 PSLE Math Prelim Q41

Jane started driving at 9.30 am from Town A to Town B. At 11.30 am, Jane had covered only 2/5 of the distance. She had to cover another 144 km before she reached Town B.

(a) What was the distance between Town A and Town B?

(b) If Jane were to travel at an average speed of 72km/h after 11.30 am, at what time would she reach Town B?
(Express your answer using the 24-hour clock)

Solution


(a)
3 units ----- 144 km
1 unit ----- 144 km divided by 3 = 48 km
5 units ----- 5 x 48 km = 240 km

Answer: 240 km


(b)
Time = 144km divided by 72 km/h = 2 h
2 hours after 11.30 am is 1.30 pm or 1330 h.

Answer: 1330 h

Anglo Chinese School 2007 PSLE Math Prelim Q48

Mr Goh was travelling from Town X to Town Y. After completing 2/7 of the journey, he passed by Mr Lee travelling the same direction. Mr Lee was travelling at an average speed of 60 km/h. Mr Goh reached his destination 3 hours later, while Mr Lee was still 45 km away from Town Y.

(a)Find the distance between the two towns.
(b)If Mr Lee left Town x at 11.30 am, what time would he arrive at Town Y?

Solution



(a)
(Goh) 5/7 of journey ----- 225 km
1/7 of journey ----- 225 km 5 = 45 km
(Whole journey) 7/7 ----- 45 km x 7 = 315 km

Answer: 315 km


(b)
Lee’s time ----- distance divided by speed
315 km divided by 60 km/h
= 5.25 hours or 5 hours 15 min

Since Lee left at 11.30 am, he would arrive at 4.45 pm.

Answer: 4.45 pm

Singapore Chinese Girls Sch 2008 PSLE Math Prelim Q44

Andrew left Town X for Town Y which was 500 km apart. He travelled at an average speed of 90 km/h for 3/5 of the journey. He then increased his speed by 30 km/h for the rest of the journey and reached Town Y at 2 pm. Richard also left Town X for Town Y at the same time as Andrew and he drove at an average speed of 100 km/h for the whole journey.

a) What time did Andrew leave Town X?
b) How far apart were they at 1 pm?

Solution



5 units ---- 500 km
1 unit ---- 500 km divided by 5 = 100 km
Every 1/5 of journey ----- 100 km

(a)
Andrew’s Time (1st 3/5 of journey) ---- distance divided by speed
= 300 km divided by 90 km/h
= 3 and 1/3 hours

Andrew’s Time (last 2/5 of journey)
= 200 km/h divided by 100 km/h
= 1 and 2/3 hours

Total time taken by Andrew ----
(3 and 1/3 hours) + (1 and 2/3 hours) = 5 hours

He reached Town Y at 2 pm.
5 hours before 2 pm is 9 am.

Answer: Andrew left Town X at 9 am.


(b)
At 1 pm, both of them travelled for 4 hours.

Richard’s distance ----- speed x time
= 100 km/h x 4 h
= 400 km


Andrew’s distance at 1 pm was ----

For the 1st 3 and 1/3 hours, he travelled 3/5 of journey ---- 300 km.

For the next 2/3 hour he travelled ---- speed x time
= 120 km/h x 2/3 h
= 80 km

Andrew’s total distance in 4 hours ----
300 km + 80 km
= 380 km


They were apart by ----
400 km (Richard’s distance) – 380 km (Andrew’s distance)
= 20 km

Answer: They were 20 km apart.

Rosyth Sch 2006 PSLE Math Prelim Q33

The graph below shows the distance traveled by Mark in 4 hours. What was Mark’s average speed?


Solution

Speed = Distance divided by time
Speed = 260 km divided by 4 h = 65 km/h (Answer)

Catholic High Sch 2006 PSLE Math Prelim Q43

At 7.30 am, Hubert left Johor, travelling towards Kuala Lumpur at a constant speed. 1 hour later, Joshua started travelling from Johor on the same road. Joshua overtook Hubert at 11.30 am. The speed at which Joshua was travelling at was 20km/h faster than Hubert and he arrived at Kuala Lumpur at 12.30pm. Find the distance between Johor and Kuala Lumpur.

Solution

Hubert’ time ----- 7.30 to 11.30 --- 4h
Joshua’s time ----- (1h later) 8.30 to 11.30 --- 3h

At the point where Joshua overtook Hubert, both travelled the same distance. However Joshua’s speed was 20km/h more than Hubert.

Hubert’s distance ----- Joshua’s distance
Hubert’s speed x Hubert’s time ------ Joshua’s speed x Joshua’s time
1 unit x 4 ----- (1 unit + 20) x 3
4 units ----- 3 units + 60
1 unit ----- 60

Joshua’s speed -----
1 unit + 20
60 + 20 = 80

Distance from Johor to KL -----
Joshua’s speed x Joshua’s time
80km/h x 4h (Joshua took from 8.30 to 12.30 to reach KL)
= 320 km (Answer)

Pei Chun Public Sch 2007 PSLE Math Prelim Q47

Najip, Kumar and Gurmit started jogging at the same time from the same starting-point round a circular track. Najip and Kumar jogged in a clockwise direction and Gurmit jogged in an anti-clockwise direction. Gurmit took 5 minutes to complete each round. Gurmit met Najip after every 3 minutes. Gurmit met Kumar after every 2 minutes. The jogging speed of each person remained the same throughout.
a) What was the ratio of Gurmit’s speed to Najip’s speed to Kumar’s speed?

b) When Gurmit and Najip met again at the starting-point after 15 minutes, Kumar had already jogged 3.6 km. What is the circumference of the circular track?



b)
(Gurmit)
5 min ----- 1 round
15 min ----- 3 rounds

Kumar (since ratio Gurmit : Kumar is 2:3) ----- 4.5 rounds
3.6 km divided by 4.5 rounds = 0.8 km per round

Answer: The circumference is 0.8 km

======

Update - 1420 hours, 29 Aug 2008

I have relabelled the model to make it clearer.
The model is seen from Gurmit’s perspective.
He was running in the opposite direction as compared to the other two.

In the 5 min cycle, Gurmit will see Kumar after 2 min.
This means G would have covered 2/5 of lap when he met K.
It also means K would have covered 3/5 lap at that point.
Hence, the model shows 2 units for G and 3 for K.

In the same 5 min cycle, G will meet N after 3 min.
This means G would have covered 3/5 lap when he met N.
Of course, N would have covered 2/5 lap.
Hence, 3 units for G and 2 for N.

Maha Bodhi Sch 2007 PSLE Math Prelim Q44

Two motorists, X and Y, travelled on the same route from Town A to Town B. They each drove at a uniform speed but started their journey at a different time of the day.

The table below shows some details of their journey.

If Motorist X reached Town B at 1625, find:
a) the distance between the two towns and
b) the speed at which Motorist Y was travelling.

Solution

a)
Consider Motorist X -----
Distance (middle portion) ----- 120 km/h x 2.5 h = 300 km
Total Distance covered ---- 60 km + 300 km + 60 km = 420 km

Answer: The total distance was 420 km.


b)
Motorist Y -----
Middle portion ----- 420 km – 100 km – 100 km = 220 km
Speed ----- 220 km divided by 2.5 hours = 88 km/h

Answer: Speed of Motorist Y was 88 km/h.

Henry Park Pri Sch 2007 PSLE Math Prelim Q48

A lorry, a van and a car set off at the same time travelling at a constant speed of 60 km/h, 80 km/h and 120 km/h respectively. The lorry and the van were travelling from Town G to Town H while the car was travelling from Town H to Town G. The car passed the lorry 2 minutes after passing the van.
a) Find the ratio of the distances travelled by the lorry to the van to the car at the moment when the car passed the van.
b) Find the distance between Town G and H.

Solution

a)
Since all of them started at the same time, the distance covered by each vehicle is proportionate to their respective speeds.

Lorry : Van : Car
60 : 80 : 120
3 : 4 : 6 (Answer)

b)
Ratio of the distance covered by the lorry to the distance covered by the car is 3:6 or 1:2. Hence, for every 2 units of distance the car travelled, the lorry travelled 1 unit.

Ratio of distance covered by the van to the distance covered by the car is 4:6 or 2:3. Hence, for every 3 units of distance the car travelled, the van travelled 2 units.



Van covered 2 units for every 3 units car covered.
Hence if the van covered 6 units, the car would have covered 9 units.

Lorry covered 1 unit for every 2 units car covered.
Hence, if the lorry covered 5 units, the car would have covered 10 units.

Distance = speed x time

The speed of the car was 120 km/h.
When the car passed the lorry, it was 2 min after it had passed the van.

Distance covered by the car within those 2 minutes ----
120 km/h x 1/30 h = 4 km

1 unit ----- 4 km

(Total distance)
15 units ----- 4 km x 15 = 60 km

Answer: The distance between Towns G and H is 60 km.

S’pore Hokkien Huay Kuan 2007 PSLE Math Prelim Q46

At 8.30 am. Tom drove from Town P to Town Q at an average speed of 80 km/h. After driving 2/5 of the journey for 4 hours, he passed Paul who was travelling along the same road in the opposite direction. Paul was travelling at a speed which was 20 km/h slower than Tom. At what time did Paul leave Town Q?

Solution



2 units ----- 320 km
1 unit ----- 320 km divided by 2 = 160 km

Distance Paul covered when he passed Tom
3 units ----- 160 km x 3 = 480 km

Time Paul took to cover 480 km -----
480 km divided by 60 km/h = 8 hours

8 hours before 12.30 pm is 4.30 am.

Answer: Paul left Town Q at 4.30 am.

Note – “The Singapore Hokkien Huay Kuan 5-School Combined Prelim Maths” is the common Maths Prelim Exam for Tao Nan, Ai Tong, Chongfu, Nan Chiau and Kong Hwa schools.

Ai Tong School P6 SA1 2006 Math (Q44)

John and Ken took part in a race. When Ken had completed the race in 20 minutes, John had only run 3/5 of the distance. John’s average speed for the race was 60 m/min less than Ken’s.
(a) Find the distance of the race.
(b) What was John’s speed in m/min?

Solution



2 units ----- 60 m/min
1 unit ----- 60 m/min divided by 2 = 30 m/min
(John’s speed) 3 units ----- 30 m/min x 3 = 90 m/min

Ken’s speed ----- 90 m/min + 60 m/min = 150 m/min
Total distance ----- John’s speed x time
= 150 m/min x 20 min = 3000 m

Answers: (a) The total distance is 3000m. (b) John’s speed was 90 m/min.

Rosyth School 2006 PSLE Math Prelim Question

Mr and Mrs Wong left their house in the same car for Town P. Mr Wong drove at a speed of 60 km/h. Realizing that he left his lap-top at the home, he let Mrs Wong alight at a bus-stop and drove back to his house. Mrs Wong walked from the bus-stop at a speed of 4 km/h to Town P. It took her 45 min to reach Town P. Both Mr Wong and Mrs Wong arrived at Town P at the same time. Find the distance between their house and Town P.

Solution

(click on image below for clearer view)

Distance (bus-stop to Town P) ---- Speed x time
= 4km/h (Mrs Wong's walking spd) x 3/4h
= 3 km (distance from bus-stop to Town P)


Time for car to travel 3 km at 60 km/h (time = distance/speed)
= (3km) divided by (60 km/h)
= 3 min

Therefore it took Mr Wong 3 min to drive from bus-stop to Town P.

Since Mrs Wong took 45 min to walk from bus-stop to Town P, it also means that Mr Wong took 45 min to travel from bus-stop to their home, and from their home to Town P.

This means that the time Mr Wong took to travel from bus-stop to his home, and from his home to bus-stop again would be -

45 min – 3 min = 42 min


Distance covered by Mr Wong during that 42 min period -

Dist = speed x time

= 60km/h x 42min

= 60km/h x (42/60)h

= 42 km

42 km is the distance from bus-stop to home, then back to bus-stop again.

But distance from home to bus stop is only half of that, which is

1/2 x 42km

= 21 km (distance from home to bus-stop)


Distance from home to Town P therefore is

21 km (distance from home to bus-stop) + 3 km (distance from bus-stop to Town P)

= 24 km

Answer: The distance between their home and Town P is 24 km.