Q&A - PSLE Math

[dnsy]

Appreciate anyone’s help on this question:


Mr lee left town M and travelled towards town N at an average speed of 80km/h. An hour later, mr Ong left town M and travelled towards town N at an average speed of 100km/h. Mr Ong passed town Q which was halfway between town M and town N 30 minutes earlier than mr Lee. If mr Ong reached town N at 10 pm , at what time did mr Lee leave town M for town N ?

Thanks!

[tianzhu]

dnsy:

Mr lee left town M and travelled towards town N at an average speed of 80km/h. An hour later, mr Ong left town M and travelled towards town N at an average speed of 100km/h. Mr Ong passed town Q which was halfway between town M and town N 30 minutes earlier than mr Lee. If mr Ong reached town N at 10 pm , at what time did mr Lee leave town M for town N ?

Hi

There are a few ways to go about this question.

For question on “Speed”, it helps to draw a simple diagram to show the relationships between two motorists on a timeline.

Using,the formula, Distance ------ Speed*Time with logical reasoning,

Head start by Mr Lee ------- 80km (1*80)

Time taken by Mr Ong to catch up with Mr Lee ------- 80/(100-80) ------- 4h

30mins -----1/2h
½ *80 -------40
40/20 ------ 2h (Mr Ong took another 2h to be 20km ahead of Mr Lee @midpoint.)

Mr Ong took a total of 6h to reach the midpoint.

Time taken by Mr Ong for the whole journey ------2*6 ------12h

Working backwards from 10pm,Mr Ong started his journey@10am

Hence, Mr Lee started @9am.

For students who are familiar with inverse proportion, here's an alternative.

From Town M ------ Town Q, Mr Ong took (1+0.5) or 1.5h less than Mr Lee.(half)
From Town M -------Town N, Mr Ong took (2*1.5) or 3h less than Mr Lee.(whole)

Speed Ratio
MrOng:Mr Lee ------ 100 :80 ------5:4

Time Ratio
MrOng:Mr Lee ------ 4:5

1 unit ----- 3h
Mr Ong ------4 units ------12h

Working backwards from 10pm,Mr Ong started his journey@10am

Hence, Mr Lee started @9am.

Best wishes

[Chan09]

Appreciate some help

A had a total of 2050 black and red marbles. He lost 3/5 of his black marbles and bought 150 red marbles. As a result the no. of red marbles he had was 1/4 of the remaining black. How many more black than red marbles he had at first?
Ans: 1950

[tianzhu]

Chan09:

Appreciate some help

A had a total of 2050 black and red marbles. He lost 3/5 of his black marbles and bought 150 red marbles. As a result the no. of red marbles he had was 1/4 of the remaining black. How many more black than red marbles he had at first?
Ans: 1950

Hi

This question was discussed in an earlier post.

Please refer to solution by MathIzzzFun.

Best wishes

http://i53.tinypic.com/2vj4ozo.jpg\">

[stary]

Hi all,


Have a question to ask.

Azman had 25% more marbles than Chongfu. Chongfu had 60% more marbles than Bala. During a game, Azman and Bala lost some marbles to Chongfu in the ratio 3:1. In the end, Azman and Bala had 780 and 480 marbles left respectively.

How many marbles did Azman have at first?

[MathIzzzFun]

stary:

Hi all,


Have a question to ask.

Azman had 25% more marbles than Chongfu. Chongfu had 60% more marbles than Bala. During a game, Azman and Bala lost some marbles to Chongfu in the ratio 3:1. In the end, Azman and Bala had 780 and 480 marbles left respectively.

How many marbles did Azman have at first?

Hi

ratio -
Azman : Chongfu =125: 100 = 5:4
Chongfu : Bala = 160 : 100 = 8: 5
so, Azman : Chongfu : Bala = 10 : 8 : 5

Before losing the marbles,
Azman : Bala = 10 : 5 = 2u : 1u

Azman and Bala lost marbles in the ratio of 3:1 and had 780 and 480 left respectively.

Azman: Bala = 2u-780 : 1u-480 = 3:1
so 2u -780 = 3u - 1440, 1u = 660

at first, Azman had 2u = 2x660 = 1320 marbles.

cheers.

[TT2]

Hi I have another qn to ask…


In Jan, 80% of the members in a golf club were men. In jun, after 55 men had left and 75 women had joined the club, the % of the women increased to 40%. How many members were there in the golf club in Jan?

Thank you

[MathIzzzFun]

TT2:

Hi I have another qn to ask...


In Jan, 80% of the members in a golf club were men. In jun, after 55 men had left and 75 women had joined the club, the % of the women increased to 40%. How many members were there in the golf club in Jan?

Thank you

Hi

In Jan, ratio of men : women : 80:20 = 4u:1u ** total 5u
after 55 men left, and 75 women joined,
ratio of men : women
= 4u - 55 : 1u + 75
= 60 : 40
= 3 : 2

so, 8u - 110 = 3u + 225
5u = 335

Members in Jan = 5u = 335

cheers.

[stary]

Thanks MathIzzzFun for your prompt reply!

[Daddy]

Hi,


Need help on this question? Thanks

John had 1.5m of copper wire. He cut some of the wire to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles and the length of XY is 19 cm. How much of the copper wire was left?

http://i55.tinypic.com/a2q0rs.jpg\">

Thanks