Q&A - PSLE Math

[faith2u]

1). In a class, there are 4 more boys than girls. 1/3 of the girls and 7/11 of the boys take the MRT train to school. If ½ of the class take the MRT, how many boys and girls are there in the class?


2). The ratio of the number of 50cent coins to the number of 10cent coins in a box was 5:3. 5-50cent coins were taken out and exchanged for 10cent coins of equal value. The money was then put back into the box. The ratio of 50cent coins to 10cent coins became 1:2.
(a). how much money was there in the box?
(b). if 10 10cent coins were taken out and exchanged for 20cent coins and the money returned to the box, what would the ratio of the number of 10centcoins to the number of 20cent coins to the number of 50cent coins be then? Give your answer in the simplest form.

Thanks.

[James Ang]

James Ang:

Practise more speed and circle questions this year.



Car A left Town X for Town Y at the same time when Car B left Town Y for Town X. The average speed of Car A was 56 km/h and the average speed for Car B was 72 km/h. The two cars passed each other at a point 24km from the midway of the two towns. What is the distance between Town X and Town Y?

2 more speed questions;

1) A car travels from Town X to Town Y at a constant speed. If the car increases its speed by 20%, it will reach Town Y one hour earlier. If the car increases its speed by 25% after travelling for 120 km, it will reach Town Y 48 minutes earlier. Find the distance between Town X and Town Y.

2) Andy and Ben started travelling at the same time from Town X and reached Town Y at the same time. During the journey, Andy spent 1/3 of Ben's travelling time resting while Ben spent 1/4 of Andy's travelling time resting. Find the ratio of Andy's speed to Ben's speed.

[James Ang]

2 more speed questions;


1) Tim walks to school from his home. One day, as he was walking pass a junction, he remembered that he left his wallet at home and he ran back to take his wallet and ran from home to school. He reached school at the same time as he usually did. The ratio of his running speed to his walking speed is 5:2. Given that the distance from the junction to his school is 1km, what is the distance between his home and school?

2) Andy, Benjamin and Charles travel from Town X to Town Y. They leave Town X at the same time. Andy drives at 56km/h, Benjamin walks at 8km/h and Charles walks at 7km/h. Andy gave Benjamin a lift at the start of journey to travel a part of the journey and then comes back to pick up Charles. They arrived at Town Y at the same time. If Benjamin walks 2.8km, how far does Charles walk?

[Tang]

James Ang:

72 - 56 = 16


24 x 2 = 48

72 + 56 = 128

16 km/h --> 48 km

1 km / h --> 48 / 16 = 3 km

128 km/h --> 128 x 3 = 384 km

The distance between the 2 towns is 384 km.


2 more speed questions;

1) A car travels from Town X to Town Y at a constant speed. If the car increases its speed by 20%, it will reach Town Y one hour earlier. If the car increases its speed by 25% after travelling for 120 km, it will reach Town Y 48 minutes earlier. Find the distance between Town X and Town Y.

Please refer to uncle Observer's blog for similar questions and answers.


2) Andy and Ben started travelling at the same time from Town X and reached Town Y at the same time. During the journey, Andy spent 1/3 of Ben's travelling time resting while Ben spent 1/4 of Andy's travelling time resting. Find the ratio of Andy's speed to Ben's speed.

TA + 1/3 TB = TB + 1/4 TA

3/4 TA = 2/3 TB

3/4 (D / SA) = 2/3 (D / SB)

SA/ SB = 3/4 x 3/2 = 9/8

The ratio of Andy's speed to Ben's speed was 9 : 8 .

[Tang]

James Ang:

Practise more speed and circle questions this year.



1) A car travels from Town X to Town Y at a constant speed. If the car increases its speed by 20%, it will reach Town Y one hour earlier. If the car increases its speed by 25% after travelling for 120 km, it will reach Town Y 48 minutes earlier. Find the distance between Town X and Town Y.

Please refer to uncle Observer's blog for similar questions and answers.

Answer is 360 km.

[Tang]

James Ang:

2 more speed questions;


1) Tim walks to school from his home. One day, as he was walking pass a junction, he remembered that he left his wallet at home and he ran back to take his wallet and ran from home to school. He reached school at the same time as he usually did. The ratio of his running speed to his walking speed is 5:2. Given that the distance from the junction to his school is 1km, what is the distance between his home and school?

DR/SR = 1/SW

DR = SR/SW = 5/2 = 2.5

Distance between home and school = (2.5 + 1)/2 = 1.75 km


2) Andy, Benjamin and Charles travel from Town X to Town Y. They leave Town X at the same time. Andy drives at 56km/h, Benjamin walks at 8km/h and Charles walks at 7km/h. Andy gave Benjamin a lift at the start of journey to travel a part of the journey and then comes back to pick up Charles. They arrived at Town Y at the same time. If Benjamin walks 2.8km, how far does Charles walk?

(D - 2.8 )/56 + (D - 2.8 - DC)/56 = DC/7
2 D - 5.6 = 9 DC

(D - DC)/56 = 2.8/8
D = 19.6 + DC
2 D = 39.2 + 2 DC (Multiply by 2)

39.2 + 2 DC - 5.6 = 9 DC
DC = 33.6/7 = 4.8 km

Charles walks 4.8 km.

See Corrections in post below - Answer 2.4 km

[James Ang]

Tang:

(D - 2.8 )/56 + (D - 2.8 - DC)/56 = DC/7

2 D - 5.6 = 9 DC

(D - DC)/56 = 2.8/8
D = 19.6 + DC
2 D = 39.2 + 2 DC (Multiply by 2)

39.2 + 2 DC - 5.6 = 9 DC
DC = 33.6/7 = 4.8 km

Charles walks 4.8 km.

1) is correct.

for 2)
Charles walks slower at 7km/h, Benjamin walks faster at 8km/h, so Charles cannot be walking more than Benjamin right? And still reach at same time

[Tang]

James Ang:

1) is correct.


for 2)
Charles walks slower at 7km/h, Benjamin walks faster at 8km/h, so Charles cannot be walking more than Benjamin right? And still reach at same time

Corrections:
------------

(D - 2.8 )/56 + (D - 2.8 - DC)/56 = DC/7
2 D = 9 DC + 5.6

(D - 2.8 - DC)/56 + (D - DC)/56 = 2.8/8
2 D = 2 DC + 22.4

9 DC + 5.6 = 2 DC + 22.4
DC = 16.8/7 = 2.4 km

Charles walks 2.4 km.

[atutor2001]

Hi Jame Ang


Is the answer 2.4km for question 2?

[Dharma]

faith2u:

1). In a class, there are 4 more boys than girls. 1/3 of the girls and 7/11 of the boys take the MRT train to school. If ½ of the class take the MRT, how many boys and girls are there in the class?



Thanks.

Hope this helps
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