Q&A - PSLE Math

[MathIzzzFun]

Winx5015:

Need help for the following questions.


(1). Alex left Town P at 7.30am and travelled towards Town Q. Jia Hao left Town Q at 8am and travelled towards Town P along the same road. Jia Hao's average speed was 10 1/2 km/h faster than Alex's average speed and he reached Town P at 12 noon while Alex was still 6km from Town Q.
(a). What was the distance between the 2 towns?
(b). At what time did Alex reach Town Q?



Thanks!

Hi

Draw a diagram so that you can visualize the parts of journey involved.

Total time taken by Jia Hao to travel from Q to P = 4h
Extra distance travelled by Jia Hao = 4 x 10.5 = 42km

When Jia Hao started at 8am, Alex has travelled for 1/2 h --> \"headstart\"
so, \"head start\" + 6 km = 42 km
\"head start\" --> 36 km --> distance covered in 1/2 h by Alex
Alex's speed --> 72 km/h
Distance between P & Q = 72 km x 4 + 42 km = 330 km

At 12noon, Alex was still 6 km from Town Q,
6 / 72 = 1/6 h = 10 min

Alex will reach Town Q at 12.10pm

cheers.

[Zack7]

lousymum:

pls help


kumar had 50% more bookmarks than leon.
max had 75% as many bookmarks as kumar.
kumar and leon gave max a number of bookmarks in the ratio 3:1.
as a result, maz had twice as many bookmakrs as before, and leon had 16 bookmarks more than kumar.
how many bookmarks did kumar give to max?

tia

hi lousymum, if i may say, for whatever reasons, i don't think you are lousy as a mum. the fact that you care for your son or daughter shows that you aren't as lousy as you think you are.

let k be kumar bookmarks

le the number of bookmarks leon gave be x

so

kumar = k
leon = (2/3)k
max = 0.75k

so after giving, leon had 16 more than kumar

(2/3 k - x) - (k - 3x) = 16 ---- equation 1

so after giving, max had twice as many as before

0.75k = 4x

solving,

k = (16/3)x

sub into equation 1

32/9 x - x - 16/3 x + 3x = 16

2/9x = 16
x =72
k= 384

so how many bookmarks did kumar give to max? = 3x = 216

[MathIzzzFun]

lousymum:

pls help


kumar had 50% more bookmarks than leon.
max had 75% as many bookmarks as kumar.
kumar and leon gave max a number of bookmarks in the ratio 3:1.
as a result, max had twice as many bookmarks as before, and leon had 16 bookmarks more than kumar.
how many bookmarks did kumar give to max?

tia

Hi

Kumar:Leon --> 3:2
Kumar:Max --> 4:3
Kumar : Leon : Max --> 12 : 8 : 9 --> 48u : 32u : 36u

Max received a total of 36u of bookmarks from Kumar & Leon in ratio of 3:1,
Bookmarks given by Kumar : Leon --> 27u : 9u
Bookmarks left, Kumar : Leon --> 21u : 23u
2u --> 16, 1u --> 8

Bookmarks given by Kumar to Max --> 8 x 27 = 216

cheers.

[Winx5015]

MathIzzzFun


:thankyou:

[Zack7]

MathIzzzFun:

lousymum:

pls help


kumar had 50% more bookmarks than leon.
max had 75% as many bookmarks as kumar.
kumar and leon gave max a number of bookmarks in the ratio 3:1.
as a result, max had twice as many bookmarks as before, and leon had 16 bookmarks more than kumar.
how many bookmarks did kumar give to max?

tia

Hi

Kumar:Leon --> 3:2
Kumar:Max --> 4:3
Kumar : Leon : Max --> 12 : 8 : 9 --> 48u : 32u : 36u

Max received a total of 36u of bookmarks from Kumar & Leon in ratio of 3:1,
Bookmarks given by Kumar : Leon --> 27u : 9u
Bookmarks left, Kumar : Leon --> 21u : 23u
2u --> 16, 1u --> 8

Bookmarks given by Kumar to Max --> 8 x 27 = 216

cheers.

short simple sweet :goodpost:

[mathnoobs]

MathIzzzFun:

lousymum:

pls help


kumar had 50% more bookmarks than leon.
max had 75% as many bookmarks as kumar.
kumar and leon gave max a number of bookmarks in the ratio 3:1.
as a result, max had twice as many bookmarks as before, and leon had 16 bookmarks more than kumar.
how many bookmarks did kumar give to max?

tia

Hi

Kumar:Leon --> 3:2
Kumar:Max --> 4:3
Kumar : Leon : Max --> 12 : 8 : 9 --> 48u : 32u : 36u

Max received a total of 36u of bookmarks from Kumar & Leon in ratio of 3:1,
Bookmarks given by Kumar : Leon --> 27u : 9u
Bookmarks left, Kumar : Leon --> 21u : 23u
2u --> 16, 1u --> 8

Bookmarks given by Kumar to Max --> 8 x 27 = 216

cheers.

I'm afraid this is very deep for me. How do I know that I have to multiply 12:8:9 by 4 ? also how do I know that I have to multiply 3:1 by 9 ?

[mathnoobs]

mathnoobs:

MathIzzzFun:

[quote=\"lousymum\"]pls help


kumar had 50% more bookmarks than leon.
max had 75% as many bookmarks as kumar.
kumar and leon gave max a number of bookmarks in the ratio 3:1.
as a result, max had twice as many bookmarks as before, and leon had 16 bookmarks more than kumar.
how many bookmarks did kumar give to max?

tia

Hi

Kumar:Leon --> 3:2
Kumar:Max --> 4:3
Kumar : Leon : Max --> 12 : 8 : 9 --> 48u : 32u : 36u

Max received a total of 36u of bookmarks from Kumar & Leon in ratio of 3:1,
Bookmarks given by Kumar : Leon --> 27u : 9u
Bookmarks left, Kumar : Leon --> 21u : 23u
2u --> 16, 1u --> 8

Bookmarks given by Kumar to Max --> 8 x 27 = 216

cheers.

I'm afraid this is very deep for me. How do I know that I have to multiply 12:8:9 by 4 ? also how do I know that I have to multiply 3:1 by 9 ?[/quote]never mind. I finally figured it out. Still very deep though.

[Zack7]

mathnoobs:

MathIzzzFun:

[quote=\"lousymum\"]pls help


kumar had 50% more bookmarks than leon.
max had 75% as many bookmarks as kumar.
kumar and leon gave max a number of bookmarks in the ratio 3:1.
as a result, max had twice as many bookmarks as before, and leon had 16 bookmarks more than kumar.
how many bookmarks did kumar give to max?

tia

Hi

Kumar:Leon --> 3:2
Kumar:Max --> 4:3
Kumar : Leon : Max --> 12 : 8 : 9 --> 48u : 32u : 36u

Max received a total of 36u of bookmarks from Kumar & Leon in ratio of 3:1,
Bookmarks given by Kumar : Leon --> 27u : 9u
Bookmarks left, Kumar : Leon --> 21u : 23u
2u --> 16, 1u --> 8

Bookmarks given by Kumar to Max --> 8 x 27 = 216

cheers.

I'm afraid this is very deep for me. How do I know that I have to multiply 12:8:9 by 4 ? also how do I know that I have to multiply 3:1 by 9 ?[/quote]
Ratios are about scaling. You don't have to multiply them, just that u will b working with fractions.

[mathnoobs]

Zack7:

Ratios are about scaling. You don't have to multiply them, just that u will b working with fractions.

yes, but it is not easy to see the scaling factor, until you go through the entire question, mull through it and figure out which numbers you need to equalize. In this case, have to scale twice, so not so easy to see upfront. I think under exam conditions, very difficult to see how to scale it so that the relevant numbers are equal. Even under non exam conditions, for me, it was difficult to see which numbers can be equalized and thus scaling is applied.

[MathIzzzFun]

mathnoobs:

Zack7:

Ratios are about scaling. You don't have to multiply them, just that u will b working with fractions.

yes, but it is not easy to see the scaling factor, until you go through the entire question, mull through it and figure out which numbers you need to equalize. In this case, have to scale twice, so not so easy to see upfront. I think under exam conditions, very difficult to see how to scale it so that the relevant numbers are equal. Even under non exam conditions, for me, it was difficult to see which numbers can be equalized and thus scaling is applied.

Hi

students learn in lower primary how to \"scale\" using models. eg. Alice had twice as much money as Mary. If they had $30 altogether, how much did each have?

The model drawing will show 2 blocks for Alice, 1 block for Mary. Total 3 blocks representing $30

eg. The number of red marbles to the number of blue marbles in a box is in the ratio of 2 : 7. If there are 63 marbles altogether, how many red marbles are there ?
The model drawing will show 7 blocks for blue marbles, 2 blocks for red marbles, total 9 blocks representing 63.

In the question above, when we arrive at the ratio Kumar: Leon: Max-->12:8:9, we can work with these numbers directly ie 12u:8u:9u

Max has 9u. Since he had twice after receiving the bookmarks from the others, he received 9u.
So, total number contributed by both kumar and leon is 9u, in the ratio of 3:1 --> back to the examples above: Kumar 3 blocks, Leon 1 block, total 4 blocks for 9u, so 1 block --> 9u/4

Kumar gave 3 blocks --> 3x 9u/4 = 27u/4
Leon gave 1block --> 9u/4

Left, Kumar : Leon --> 12u-27u/4 : 8u-9u/4 --> 21u/4 : 23u/4 --> 21u:23u ... so we get to the same final ratio. the only difference is that when we work with the numbers directly, we will have to work with fractions - which many students dislike

good night !

cheers.