Q&A - PSLE Math

[Winx5015]

tianzhu,


Really appreciate your help

[tianzhu]

YumYum:

Hi, can anyone pls help with this Qn?


A bus was scheduled to travel from Town X to Town Yat a fixed speed, V km/h.
If the speed of the bus was increased by 20%, it could arrive at Town Y 80 minutes ahead of schedule. Instead, if the bus travelled the first 275 km at V km/h and after that it increased the speed by 25%, it could reach Town Y 30 mins ahead of schedule. Find the dustance between the 2 towns.

thanks!

Hi

The answer is 400km.

This is definitely not a PSLE type of Speed question.

Where is this question from?

Best wishes

[Chan09]

Hi, need some help on this:

Area of triangle is 1/3 the area of the square. After the shaded area is removed, the unshaded area of the square becomes 4 times the unshaded area of the triangle. Given that the unshaded area is 81cm2, find the length of the square?

The picture for this question shows a triangle and square with the square overlapping one corner of the triangle.
Ans: 27cm

Thank u.

[YumYum]

Hi Tianzhu,


the Qn is adapted from a math Olympiad Qn given to students in the school MO class. Not sure if this is the right forum to post this as I thought it’s related to speed but wasn’t aware that it’s not in PSLE syllabus…

Do you mind explaining how the answer is derived?

Thanks!

Thanks

[tianzhu]

Ngserene617:

Hi, I need help on this question:

1. When a tank is 1/3 filled with water. It weighs 58kg. If it is 3／4 filled with water, it weighs 108kg.
a) What is the weight of the empty tank?
b) What is the weight of the tank when it is completely filled with water?

Thanks...

Hi

1/3 ------ 4 units

Tank + 4 units ------ 58

3/4 ----- 9 units

Tank + 9 units ------ 108

5 units ------- 108 – 58 ------ 50

1 unit ------ 10kg

Tank ------- 58 – 40 ------ 18kg

12 units ------ 120

When the tank is completely filled with water, the weight is 120+18 ------138kg

Best wishes

[tianzhu]

Chan09:

Hi, need some help on this:

Area of triangle is 1/3 the area of the square. After the shaded area is removed, the unshaded area of the square becomes 4 times the unshaded area of the triangle. Given that the unshaded area is 81cm2, find the length of the square?

The picture for this question shows a triangle and square with the square overlapping one corner of the triangle.
Ans: 27cm

Thank u.

Hi

Please check your question.

I think the shaded area is 81 cm2 instead of the unshaded area.

Best wishes

[MathIzzzFun]

YumYum:

Hi, can anyone pls help with this Qn?


A bus was scheduled to travel from Town X to Town Yat a fixed speed, V km/h.
If the speed of the bus was increased by 20%, it could arrive at Town Y 80 minutes ahead of schedule. Instead, if the bus travelled the first 275 km at V km/h and after that it increased the speed by 25%, it could reach Town Y 30 mins ahead of schedule. Find the dustance between the 2 towns.

thanks!

Hi

using speed & time ratio...

Time taken for whole journey at V km/h : 1.2V km/h = 6:5 = 48u : 40u
8u --> 80 min, 1u --> 10 min
30 min --> 3u
Time taken for 2nd part of journey at V km/h : 1.25V km/h = 5 : 4 = 15u : 12u
So, time taken for 275km --> 48u - 15u = 33u
Total time taken for whole journey at V km/h --> 48 u
48 /33 x 275 = 400km --> total distance between X and Y = 400 km

cheers.

[MathIzzzFun]

Chan09:

Hi, need some help on this:

Area of triangle is 1/3 the area of the square. After the shaded area is removed, the unshaded area of the square becomes 4 times the unshaded area of the triangle. Given that the unshaded area is 81cm2, find the length of the square?

The picture for this question shows a triangle and square with the square overlapping one corner of the triangle.
Ans: 27cm

Thank u.

Hi

81 cm2 should be 810 cm2 ?

cheers.

[Chan09]

Hi Tianzhu,

Apologies. Yes shaded area is 81cm2? Rest of question is correct.

Can u advise how to solve, thank you.

[MathIzzzFun]

Chan09:

Hi Tianzhu,

Apologies. Yes shaded area is 81cm2? Rest of question is correct.

Can u advise how to solve, thank you.

Hi
unshaded square : unshaded triangle --> 4u : u
square --> 4u + 81
triangle --> u + 81
square = 3 x triangle
so, 4u + 81 = 3u + 3 x 81
1u = 2 x 81
square --> 4u + 81 = 4x2x81 + 81 = 9 x 81
each side = 3 x 9 = 27

cheers.