Q&A - PSLE Math

[MathIzzzFun]

Hi! please help

In a time trial a cyclist wanted to reach an average of 25km per hour between two towns A and C which are 10km apart. A village, B, is sited exactly halfway between A and C and is reached after a long climb up from A. When the cyclist had climbed up to B she calculated that her average speed so far was only 20km per hour. How fast must she ride on the descent from B to C if she is to attain the overall average speed of 25km per hour?

The distance between A and C need not be given, it is redundant.

Since the distance is given it is easier to work....

Average speed = total distance/total time.
so, total time taken for the trial = 10/25 h = 0.4h

Time from A to B
= distance AB/average speed from A to B
= 5/20 h
= 0.25h

Therefore, the time remaining to complete B to C
= 0.4h - 0.25h
= 0.15h

Average speed for B to C
= distance BC /time taken for BC
= 5/0.15 km/h
= 33 1/3 km/h

suppose the distance A to C is not given, then we can make use of speed ratio/ time ratio to work ie ratio of the speeds = inverse ratio of the time taken ...
for the SAME distance D,
S1 : S2 = T2 : T1
where T1 is the time @speed S1 and S2 is the time taken @speed S2 to cover the SAME distance D.

for distance AB,
ratio of target average speed : achieved speed
= 25 : 20
= 5 : 4

this means the corresponding time taken to cover AB (= inverse of the speed ratio)
@25km/h : @20km/h = 4u : 5u

since distance BC = distance AB, then
time taken to cover BC @25km/h = 4u
--> total time for distance AC = 8u @25km/h

so, to achieve target average speed of 25km/h from A to C, then remaining time for distance BC = 8u - 5u = 3u

for distance BC,
time taken @required speed : time taken @target speed of 25 km/h
= 3u : 4u
so,
required speed : target speed @25km/h
= 4 : 3 (inverse of the time ratio)

or required speed = target speed x 4/3 = 25 x 4/3 km/h = 33 1/3 km/h

cheers.

[Sruthi]

Thank you so much for your help

[forestcadee]

Hi, need some help for the following question. Is there any other ways instead of using algebra method.

1) Jack and Ellse have some stamps. If Jack gives 5 stamps to Ellse, the ratio of Jack's stamps to Ellse's is 2:5. If Ellse gives 11 stamps to Jack, the ratio of Jack's stamps to Ellse will be 2:3. How many stamps does Jack have?

Thanks.

[belnanna]

Please help on this question. Appreciated deeply! Thanks in advance!

Mrs Amos baked 30 more chocolate cookies than almond cookies.After selling 2/5 of the chocolate cookies and 3/4 of the almond cookies, she had 39 more chocolate cookies than almond cookies left. How many chocolate cookies did she bake at first?

[SAHMom]

Please help on this question. Appreciated deeply! Thanks in advance!

Mrs Amos baked 30 more chocolate cookies than almond cookies.After selling 2/5 of the chocolate cookies and 3/4 of the almond cookies, she had 39 more chocolate cookies than almond cookies left. How many chocolate cookies did she bake at first?

5C-4A=30......(1)

Remainder:
3C-1A=39
12C-4A=156.....(2)

(2)-(1):
7C=126
C=18, A=15
5C+4A=90+60=150

Or let Almond cookies be 20u, chocs 20u+30
Remainder is 5u of Almond and 12u+18 of chocs
Difference is 7u+18,=39
u=3
Total 40u+30=150

[ozora]

Need some guide on the following questions:
1. There were 9750 people at the national stadium.
3/5 of the female spectators were children and
1/4 of the male spectators were children.
There were 3 times as many male adults as female adults.
How many adults were there at the stadium?
* I couldn't get an positive answer either using model or branching method. Is there an error in this question?

2.Linda received 291 pieces of $5 and $10 notes from her redpackets she collected.
Her mother gave her 15 more pieces of $10 notes and she spent 1/4 of her $5 notes.
In the end, the number of $10 notes she had was 1/6 of the number of $5 notes.
How much did she receive in total as red packets

is the $10->$870
$5->$1020

3. Zhi wei and Weijie had total of 576 marbles.
Zhi wei lost 1/3 of his marbles to Weijie
Weijie lost 2/5 of his marbles to Zhiwei.
In the end, they each ended the same number of marbles.
How many marbles did they each have at first?
working backwards:
is the answer Zhiwei: 144
weijie:432.
Thanks for the help

[speedmaths.com]

Need some guide on the following questions:
1. There were 9750 people at the national stadium.
3/5 of the female spectators were children and
1/4 of the male spectators were children.
There were 3 times as many male adults as female adults.
How many adults were there at the stadium?
* I couldn't get an positive answer either using model or branching method.
Is there an error in this question?


Thanks for the help

Hi ozora,

Question looks okay.

(How many adults were there at the stadium?)
You should get 4500 male adults + 1500 female adults
= 6000 adults.

Please let us know if you still need help.

Cheers


Speed Maths
.

[Ender]

Hi, need some help for the following question. Is there any other ways instead of using algebra method.

1) Jack and Ellse have some stamps. If Jack gives 5 stamps to Ellse, the ratio of Jack's stamps to Ellse's is 2:5. If Ellse gives 11 stamps to Jack, the ratio of Jack's stamps to Ellse will be 2:3. How many stamps does Jack have?

Thanks.

I'm getting fraction and decimal for the answer..Something wrong..

Should it be 12 stamps instead of 11? In this case I can get the answer 35 stamps for Jack.

[Ender]

Need some guide on the following questions:
2.Linda received 291 pieces of $5 and $10 notes from her redpackets she collected.
Her mother gave her 15 more pieces of $10 notes and she spent 1/4 of her $5 notes.
In the end, the number of $10 notes she had was 1/6 of the number of $5 notes.
How much did she receive in total as red packets

is the $10->$870
$5->$1020

Work backwards

Code: Select all

     $10      $5
      1u      6u ->this is 3/4
      1u      8u ->this is 4/4, before she spent 1/4 of $5

9u = 306 pieces, after her mom gave extra 15 more notes (291+15=306).
u=34

Number of $10 = 1u =34. But as red packet she receive 19 pieces.
number of $5 = 8u = 272 pieces

Value as red packet received = $10X19 + $5X272= $1550

[Ender]

3. Zhi wei and Weijie had total of 576 marbles.
Zhi wei lost 1/3 of his marbles to Weijie
Weijie lost 2/5 of his marbles to Zhiwei.
In the end, they each ended the same number of marbles.
How many marbles did they each have at first?
working backwards:
is the answer Zhiwei: 144
weijie:432.
Thanks for the help