Tutor MathsGuru: Ask me for your burning Maths questions!

[YLH88]

[quote]
1) For time questions, is it true that the answer must be left in fraction and not decimal ? My DS wrote the answer as 37.5 h and the teacher marked him wrong. She said the answer should be 37 1/2 h. Thus, would like to check what is the practice for PSLE ? which is correct in PSLE context, 37.5 h or 37 1/2 h ?[/quote]Hi,

Regarding the question on whether to leave the time in fraction or decimal, I'm not able to get through MOE hotline, but I have consulted few teachers. Their answer are the same : Should leave the time answer in fraction even if it is 1/2 hr. Most of the time, the teacher will advise the students not to leave in decimal unless the question said so.

Regards

[Vanilla Cake]

YLH88:

1) Ali and Boris walked from their homes to school.

Ali started walking from point X at a speed of 120 m/min.At 9.05am, Ali reached point Y and at the same time Boris started walking from Point Y towards the school.At 9.15am, Boris was 100m ahead of Ali.
a) Find Boris's speed
b) If Boris reached the school 2 min ahead of Ali, find the distance Boris covered from point Y to the school. Express your answer in kilometres.

From 9.05 am to 9.15 am, time = 10 min
Distance travelled by Ali @ 120 m/min from Pt Y= 120 m/minx10min = 1200 m
Distance travelled by Boris from Pt Y = (1200+100)m = 1300m
(a) Boris average speed = 1300÷10 = 130 m/min

Distance between Pt Y to school = D
D/130+2 = D/120
(D+260)/130 =D/120
130D=120D+31200
10D=31200
D=3120m = 3.12 km
(b)Distance between Boris covered from point Y to the school = 3.12 km

OR

Ratio of speed
Ali : Borris
120 : 130
12 : 13

Ratio of time
Ali : Borris
13 : 12

Difference = (13-12)u = 1u = 2min ( Boris reached the school 2 min ahead of Ali)
For Ali's case @ 120 m/min, distance travelled = 13ux120=13x2x120=3120m = 3.12 km
For Borris's case @ 130m/min, distance travelled = 12ux130 =12x2x130=3120m = 3.12 km

YLH88:

2) A car and a lorry were heading from Town A to Town B. When the car overtook the lorry, they were 375 km away from Town B.
The car arrived 1 h 15min earlier than the lorry which was still 75 km away from Town B.
a) Find the average speed of the lorry.
b) Find the average speed of the car.

1 h 15 min = 1¼h
75÷1¼h=60 km/h
(a) Average speed of lorry = 60 km/h

375÷60=6¼h
6¼h-1¼h=5h
(b) Average speed of car = 375÷5 = 75 km/h

[Vanilla Cake]

YLH88:

4) At 11am, Mrs Chong left Town X for Town Y, driving at a constant speed.2 hours later, Mrs Tan also left Town X for Town Y.At 5pm, Mrs Tan overtook Mrs Chong.The average speed of Mrs Tan was 32 km/h faster than the average speed of Mrs Chong.

a) Find the average speed of Mrs Chong.
b) Mrs Tan was 26 km away from Town Y at 5pm. Find the distance between Town X and Town Y.

Headstart by Mrs Chong was 2 hours ahead of Mrs Tan and Mrs Tan took 4 hours to catch up with Mrs Chong. (average speed of Mrs Tan was 32 km/h faster than the average speed of Mrs Chong)

Distance travelled by Mrs Chong in 2 hours = 32x4=128 km
(a) Average speed of Mrs Chong was 128÷2 = 64 km/h

Time taken for Mrs Chong from 11 am to 5 pm = 6 hours
Distance travelled by Mrs Chong in 6 hours = 6x64 = 384 km
(b) Distance between Town X and Town Y = 384km+26km = 410 km

[Herbie]

I have a question which need help. ACS 2009 Paper 2 Q18


There are some black and white marbles in a bag.
If 20 black marbles are removed from the bag, the total number of marbles left will be 7 times the no. of black marbles left.
If 50 white marbles are removed from the bag, the total number of marbles left will be 5 times the number of black marbles left.

How many marbles are there in the bag?

Tx

[Vanilla Cake]

YLH88:

5) A car, travelling at a constant speed, took 9 hours to travel from Town Y to Town Z.A lorry, travelling at a constant speed, took 18 hours to travel from Town Z to Town Y.Both vehicles started at the same time and they met when they were 180 km from Town Z.

a) Find the distance between the two towns.
b) Find the speed of the car.

Apply constant distance concept for this question.
Car
L: Lorry

Ratio of time
C : L
9 : 18
1 : 2

Ratio of speed
C : L
2 : 1

Meeting pt was 180 km from Town Z means 1u=180 km
(If necessary, draw your own model to let you visualise better)
From Town Y to meeting pt (2u) and from meeting pt to Town Z (1u).
Since u = 180 km, 3u = 540 km
(a)Distance between the two towns was 540 km

Since total distance was 540 km and car took 9 hours, constant speed of car = 540÷9 = 60 km/h
(b) Constant speed of car = 60 km/h

YLH88:

6) Mark can climb uphill at an average speed of 2km/h and go downhill at an average speed of 6km/h. Going first uphill and then downhill, without stopping and using the same route, what will his average speed be for the entire trip ?

Assume the distance of the route be unit.
Total time taken = unit/2 + unit/6 = 4units/6 = 2units/3
Distance = 2units (climb uphill and go downhill)
Average speed = 2units÷2 units/3 = 2unitsx3/2units = 3 km/h

This is similar to NMOS 2009 Prelim round Q3. Where is this question taken from?

YLH88:

7) Wei Qiang walked up a flight of steps at an average speed of 50 m/min.When he reached the top, he ran down the same flight of steps at a speed of 200 m/min. If he took a total of 1 min to walk up and run down, how many seconds did he take to walk up the flight of steps ?

Constant distance
Ratio of speed
50 : 200
1 : 4

Ratio of time
4 : 1
Multiply by 4 (Explanation and not part of workings)
48 : 12 (Explanation and not part of workings)

(48+12)seconds= 60 seconds ie he took a total of 1 min to walk up and run down.This is an explanation and not part of the workings.

5u = 60 seconds
u = 12 seconds
4u = 12x4 = 48 seconds

Number of seconds for him to walk up the flight of steps = 48

This is an interesting question and psl advise the source.

[corneyAmber]

Almighty:

Almighty:

Hi Almighty,


The reason why you calculate the clothes $ wrongly because the \"of it\" in both instances refer to the total salary $3600. So you must take 1/3*3600 instead of 1/3*360(which is the $$ for food only)

[as 1/3 more than the mnthly salary.I dont want this mistake of mine in reading 2 b repeated.Any help to explain?

Hi Almighty,

You must be careful with this word \"more\"
When we say Ahmad has 3 times more stamps than Ali, it means Ahmad has 4 parts and Ali 1 part. This more is applied between Ahmad and Ali, so Ahmad has xxx stamps more than Ali.

In that question you posed, the total is given as a finite salary. So a fraction more of the salary spent has to be confined within the salary amount and cannot be interpreted to go beyond the amount. So it cannot go more than the salary. GWIM?

[Vanilla Cake]

Herbie:

I have a question which need help. ACS 2009 Paper 2 Q18


There are some black and white marbles in a bag.
If 20 black marbles are removed from the bag, the total number of marbles left will be 7 times the no. of black marbles left.
If 50 white marbles are removed from the bag, the total number of marbles left will be 5 times the number of black marbles left.

How many marbles are there in the bag?

Tx

Pls refer to http://prischoolmaths.blogspot.com/2009/09/acs-whole-number.html

[corneyAmber]

Herbie:

I have a question which need help. ACS 2009 Paper 2 Q18


There are some black and white marbles in a bag.
If 20 black marbles are removed from the bag, the total number of marbles left will be 7 times the no. of black marbles left.
If 50 white marbles are removed from the bag, the total number of marbles left will be 5 times the number of black marbles left.

How many marbles are there in the bag?

Tx

B=black marbles left in bag in first scenario

7B + 20 = 5(B+20) + 50
7B+20 = 5B + 100 + 50
2B = 130
B = 65

Total marbles = 7*65+20 = 475 marbles

[Vanilla Cake]

YLH88:

3) Car A and Car B left Town Y at the same time, heading in the opposite direction.Car A headed for Town Z while Car B left for Town X.The speed of Car B was 20 km/h faster than Car A. After 1/2 h, Car A had completed 2/3 of its journey while Car B had completed 1/2 of its journey.The two cars were also 110 km apart.

a) Calculate the speed of Car A.
b) How far was Car B from Town X when Car A reached its destination ?

Vanilla Cake:

½ of distance between Town X and Town Y = (110+10)÷2=60 km
⅔ of distance between Town Y and Town Z = 60-10 = 50 km
Since Distance travelled in ½ h = 50 km,
(a) Constant speed of Car A = 50x2 = 100 km/h

Distance between Town Y and Town Z = 50/2x3 = 75 km
Time taken for Car A = 75÷100 = 3/4h
Distance drove by Car B in 3/4h = 3/4x(100+20) = 3/4x120 = 90 km
Distance between Town X and Town Y = 60x2 = 120 km
120-90 = 30 km
(b) Car B was 30 km from Town X when Car A reached its destination.

Hope someone can forward with a pictorial distance-time travel diagram and easier method to help you.
May I know where are all these 7 speed questions taken from?

Hi YLH88,
http://psle2010a.blogspot.com/2010/06/speed-p6_12.html to help you understand better.

[YLH88]

Hi VC,


Thank you for the solution. These are from his school worksheets for the holiday… He has no choice but to do because his mummy very kiasu and worried about his PSLE.

Thank you!!