Tutor MathsGuru: Ask me for your burning Maths questions!

[YLH88]

Hi all,


Need help in the below question :

Sam and Harry started running at the same time from the opposite ends of the diameter of a circular track.
Both of them were running in the clockwise direction.
Sam took 12 minutes to run round the track once while Harry took 15 minutes to do the same.
How long did Sam take to run past Harry for the first time ?
(ans : 30 minutes)

http://postimage.org/image/1z70q6hqc/

Thank you!

[capricorn28]

Hi iFruit


Thank you for the clear explanation.

Best regards
Capricorn28

[capricorn28]

Hi All,


Need help on Catholic High School P5 SA2 - Year 2009
Paper 2 - Q6 and the ans is 16 degrees
Paper 2 - Q8 and the ans is 72%
Paper 2- Q13 and the ans is 80cm
Paper 2 - Q14 and the ans is 40.5cm sq
Paper 2 - Q15 and the ans is $360
Paper 2 - Q17 and the ans is 120

http://postimage.org/image/jk1hymuc/

http://postimage.org/image/s3ym9sis/

http://postimage.org/image/240e8e9fo/

http://postimage.org/image/jk4t1btw/

http://postimage.org/image/jk6gkobo/

http://postimage.org/image/2aopcqyys/
[/img][/list]

[Vanilla Cake]

capricorn28:

Hi All,

Actual workings from DD2.


VC's mum

capricorn28:

Paper 2 - Q6 and the ans is 16 degrees

http://postimage.org/image/s3ym9sis/
Angle TUV =180⁰-60⁰=120⁰
Angle XWT=180⁰-170⁰=10⁰
360⁰-60⁰=300⁰
Angle XUT =360⁰-300⁰-34⁰-10⁰=16⁰

Angle XUT = 16⁰.

capricorn28:

Paper 2 - Q8 and the ans is 72%

http://postimage.org/image/240e8e9fo/
Before
L: 4u
F: 6u

After
L: 3.2u
F: 4u

(3.2u+4u)/10ux100% = 72%

72% of the stamps was left.

capricorn28:

Paper 2- Q13 and the ans is 80cm

http://postimage.org/image/jk1hymuc/
5u=8000 cm²
4u=6400 cm²
Square root of 6400 cm² = 80 cm

Length of the square = 80 cm.

capricorn28:

Paper 2 - Q14 and the ans is 40.5cm sq

http://postimage.org/image/jk6gkobo/
24÷8x5=15 cm
24-15 = 9 cm
40-9 = 31 cm
½x40x15 = 300 cm²
½x31x9 = 139.5 cm²
½x24x40 = 480 cm²
480-139.5-300=40.5 cm²

Shaded area = 40.5 cm²

capricorn28:

Paper 2 - Q15 and the ans is $360

http://postimage.org/image/2aopcqyys/
Before
J: 6u
K: 5u

After
J: 3.6u
K: 7.4u

In the end
J: 7.3u
K: 3.7u

7.3u-3.7u=3.6u
3.6u=$216
6u = $360

At first, Jude had $360.

capricorn28:

Paper 2 - Q17 and the ans is 120

http://postimage.org/image/jk4t1btw/
Hall (2n)
B : G
3u/4 : u/4
3 : 1
15 : 5

Canteen (1n)
B : G
2p/5 : 3p/5
2 : 3
4 : 6

1u=6
20u=120

Number of pupils in the hall = 120.

[Vanilla Cake]

wkong:

The figure is not drawn to scale. It shows a rectangle divided into 6 parts. Each part has a different area.

a) Find the total area of P and Q.
b) Find the perimeter of the figure.

http://www.postimage.org/

Use guess and check,
Area of P = 8 cmx 6 cm = 48 cm²
Area of Q = 5 cm x 4 cm = 20 cm²
(a) Total area of P and Q = (48+20) cm² = 68 cm²

Length of rectangle = (5+6+4) cm = 15 cm
Breadth of rectangle = (8+5) cm = 13 cm
(15x2)+(13x2) = 30+26 = 56 cm
(b) Perimeter of the figure = 56 cm

[youngtay]

kancheongmum Thanks for your help.


Best wishes

[wkong]

Thanks again VC for your help

[Vanilla Cake]

YLH88:

Hi all,

Need help in the below question :

This is an interesting question but nobody has forward his/her solution yet.I am not please with my algebra method and let's hope that others will forward with better methods for sharing and learning.Could you pls advise the source of this question?

VC's mum

YLH88:

Sam and Harry started running at the same time from the opposite ends of the diameter of a circular track.
Both of them were running in the clockwise direction.
Sam took 12 minutes to run round the track once while Harry took 15 minutes to do the same.
How long did Sam take to run past Harry for the first time ?
(ans : 30 minutes)

http://postimage.org/image/1z70q6hqc/

LCM of 12 and 15 is 60.
Work out 60m as the length (circumference) of the circular track even though 60m is not a realistic number.
Sam's average speed = 60m÷12 = 5 m/min
Harry's average speed = 60m÷15 = 4 m/min

Note that both of them started running at the same time from the opposite ends of the diameter of a circular track means the difference in their distance = ½x60m = 30 m.
For them to meet for the first time, Sam must run more than Harry by 30 m in the same amount of time.

Assume the time taken to be T,
5xT= (4xT)+30
5T=4T+30
T=30

Sam took 30 min to run past Harry for the first time.

[YLH88]

Vanilla Cake:

YLH88:

Hi all,

Need help in the below question :

This is an interesting question but nobody has forward his/her solution yet.I am not please with my algebra method and let's hope that others will forward with better methods for sharing and learning.Could you pls advise the source of this question?

VC's mum

YLH88:

Sam and Harry started running at the same time from the opposite ends of the diameter of a circular track.
Both of them were running in the clockwise direction.
Sam took 12 minutes to run round the track once while Harry took 15 minutes to do the same.
How long did Sam take to run past Harry for the first time ?
(ans : 30 minutes)

http://postimage.org/image/1z70q6hqc/

LCM of 12 and 15 is 60.
Work out 60m as the length (circumference) of the circular track even though 60m is not a realistic number.
Sam's average speed = 60m÷12 = 5 m/min
Harry's average speed = 60m÷15 = 4 m/min

Note that both of them started running at the same time from the opposite ends of the diameter of a circular track means the difference in their distance = ½x60m = 30 m.
For them to meet for the first time, Sam must run more than Harry by 30 m in the same amount of time.

Assume the time taken to be T,
5xT= (4xT)+30
5T=4T+30
T=30

Sam took 30 min to run past Harry for the first time.

Hi VC's mum,

Thank you for the solution. But I find it a bit difficult to explain to my DS on this.

This question is taken from the A star booklet on Rate and Speed.

[kancheongmum]

YLH88:

Hi all,


Need help in the below question :

Sam and Harry started running at the same time from the opposite ends of the diameter of a circular track.
Both of them were running in the clockwise direction.
Sam took 12 minutes to run round the track once while Harry took 15 minutes to do the same.
How long did Sam take to run past Harry for the first time ?
(ans : 30 minutes)

http://postimage.org/image/1z70q6hqc/

Thank you!

Hi YLH88

This is catching up question without the distance given. I too had a hard time explaining to my DS. Let me try and see it helps.

Sam took 12 min to complete one round
Harry took 15 min to complete one round
So Sam is for sure faster than Harry
We name Sam starting point S and Harry starting point H
We imagine both Sam and Harry start from point S. Harry start running first and when he reached point H, then Sam start running. So Sam has half the circular track to catch up.

Time ratio --- Sam: Harry ---- 12 : 15 ----4:5
Same distance, constant speed, time ratio is inversely proportional to distance ratio and speed ratio
distance ratio --- 5:4
5u - 4u = 1u ---- 1/2 of the track
When Sam past Harry the 1st time Sam would have run

1/2 x 5 = 5/2 or 2 1/2 of the track
He would take --- 5/2 x 12 min = 30 mins

You can also use Harry to get the answer
When Sam past Harry the lst time Harry would have run

1/2 x 4 = 2 round
He would take --- 2 x 15 min = 30 mins

hope this help