Tutor MathsGuru: Ask me for your burning Maths questions!

[tiger262]

Dharma:

tiger262:

Can anyone post a solution for this speed question?


Kumar and Clara started jogging along a circular track.
Kumar started at Point M while Clara started at Point N where the line MN formed the diameter of the circle.
Kumar and Clara jogged toward each other along the circular track from their respective starting point and first met at Point P which was 80 m from Point M.
After they met for the first time, they continued jogging along the track and finally met again for the second time at Point Q which was 60 m from Point N. Find the distance of the circular track.

Thank you so much.

When Kumar met Clara for the 1st time at P ; he had jogged for 80m from M.
When Kumar met Clara for the 2nd time at Q; he would have jogged another 160m (2 x 80m) from P.

So, distance from P ->N -> Q = 160m
Distance PN = 160m – 60m = 100m
Circumference of the jogging track = 2 x (80m + 100m) = 360m

Dear Dharma,

You are a genius. Not only because you solve complex problems with such simple steps. But because of the way you explain the concepts and the amount of time you spare to this forum.

I wish that Maths teachers in Primary schools undergo an orientation course under your command.

Thank you so much. I am most grateful.

[Dharma]

Herbie:

Hi Dharma,


I dun understand this para \"Speed ratio = Distance ratio provided time is constant.\"

What do u mean by Time is constant?

I read the following from a book, and is says
If the travelling time of 2 individuals are the same (common time), the ration of distance covered is directly proportional or the same as the ration of the individual's speed

eg.
Speed (R) : Speed (S)
2 : 3

Time (R) : Time (S)
2 : 3

I dun understand the above mentioned theory, would you to able to explain??

Cos I tot Speed ratio is inversely proportional to Time Ratio.



Many thanks!

Hi Herbie,

Time is constant/fixed means the same as the explanation you have read from the book.

There seems to be a flaw in the example above. I believe that this is a case where the distance travelled by the 2 objects is fixed ( both travel same distance).

If you are given 2 cars travelling the same distance (fixed/constant distance) at 40km/hr and 60km/hr respectively, the speed ratios of the 2 cars are as follows: -

The speed ratio => Car A : Car B = 2 : 3

However, we know that by travelling the same distance, the slower car will take a longer time to complete the same journey as compared to a faster car.

So, the time ratio => Car A : Car B = 3 : 2

When distance is fixed (both objects travel the same distance); the speed ratio and the time ratio are inversely proportional to each other.

Lets go thru the speed question you had asked earlier

Sam took 5 hours to travel from Town A to Town B.
Ruth started at the same time as Sam and took 3 hours to drive from Town B to Town A.
When they met each other, they were 30km away from the midpoint of Town A and Town B.

What is the distance btw Town A and Town B?
What was Sam's average speed?

For this question; we actually solve the question in a few steps.

•\tWe are given time taken for Sam and Ruth to travel between 2 towns. Here distance travel is fixed (same distance). By using the time ratio of 5 : 3; we can find the speed ratio of 3 : 5 (inversely proportional)

•\tNow we know the speed ratios of Sam and Ruth and we also know that their speed is constant throughout the journey.

•\tNow, when Sam and Ruth move towards each other and meet; time is constant (both took the same time to reach the meeting point). So, now we already know the speed ratios of Sam to Ruth and we use it to find the distance ratio of Sam to Ruth. We know if time travel is the same, the faster object will travel further compared to the slower object. So, distance ratio of Sam : Ruth is 3 : 5

We need to used the relationship between speed , time and distance appropriately based on the question.

DISTANCE = SPEED X TIME

[Herbie]

Hi Dharma,


Thanks for being so patience. Yr explanation is fantastic! Really appreciate yr help!

I can understand the inverse theory for Speed and Time.
However and I am just confused with the eg. below.

eg.
Speed : Speed (S)
2 : 3

Time : Time (S)
2 : 3

Tx

[Dharma]

Herbie:

Hi Dharma,


Thanks for being so patience. Yr explanation is fantastic! Really appreciate yr help!

I can understand the inverse theory for Speed and Time.
However and I am just confused with the eg. below.

eg.
Speed (R) : Speed (S)
2 : 3

Time (R) : Time (S)
2 : 3

Tx

Hi Herbie,

Distance = Speed x Time

Speed and time is ALWAYS inversely proportional to each other if Distance is constant.

Your example does not hold because it says that speed and time are directly proportional; which in fact is not true.

If Speed ( R ) : Speed ( S) = 2 : 3
Then,

Time ( R) : Time (S) = 3 : 2

[Dharma]

super star:

Hi Mathsguru

thanks for ur help.I have another problem pls help to solve this
Aurdrey & belle have some money each.If audrey spends $18 &belle spends $24 each day,audrey will still have $25 left when belle has spent all her money.If audrey spends $13 &bellespends $30each day,audrey will have $139 left when belle has spent all her money.How much money do they have altoghter?

If Audrey spends $18/day and Belle spends $24/day in M days ;

Amt they had at first
Audrey : $25 + $18M
Belle : $24M

If Audrey spends $13/day and Belle spends $30/day in N days ;

Amt they had at first
Audrey : $139 + $13N
Belle : $30N

24M = 30N
4M = 5N

25 + 18M = 139 + 13N
50 + 36M = 278 + 26N
50 + 45N = 278 + 26N
19N = 228
N = 12days

Amt of money altogether = $139 + $43(12) = $655

[firebird]

Dear Maths guru


Good morning.

Please help me on the following question:

Keane bought some marbles and gave half of them to Leon. Leon bought some stamps and gave half of them to Keane.

Keane used 5 stamps and Leon gave away 11 marbles. The ratio of the number of stamps to the number of marbles Keane had left then became 1:7 and ratio of the number of stamps to the number of marbles Leon had left became 1:5.

How many sramps did Leon buy?

Thank you.
Firebird

[ruyu]

firebird:

Dear Maths guru


Good morning.

Please help me on the following question:

Keane bought some marbles and gave half of them to Leon. Leon bought some stamps and gave half of them to Keane.

Keane used 5 stamps and Leon gave away 11 marbles. The ratio of the number of stamps to the number of marbles Keane had left then became 1:7 and ratio of the number of stamps to the number of marbles Leon had left became 1:5.

How many sramps did Leon buy?

Thank you.
Firebird

lol like last year kim and jim question where you get this?

[firebird]

Dear ruyu


The question posted by me was given from my child’s class.

Kindly help

Thank you.
Firebird

[Almighty]

Hi Dharma / MAthguru,


http://www.postimage.org/image.php?v=gxiHqdA

1) Is my answer for Qt:12 right? I need a clarification on one thing in this problem.
The shaded length of the first square is 6 cm, how can the whole length of the second square also be 6 cm? (Marked in pencil)
2)Circle question.Unable to get a hint 2 do this.Any help?

[Almighty]

firebird:

Dear Maths guru


Good morning.

Please help me on the following question:

Keane bought some marbles and gave half of them to Leon. Leon bought some stamps and gave half of them to Keane.

Keane used 5 stamps and Leon gave away 11 marbles. The ratio of the number of stamps to the number of marbles Keane had left then became 1:7 and ratio of the number of stamps to the number of marbles Leon had left became 1:5.

How many stamps did Leon buy?

Thank you.
Firebird

Hi Fire Bird,

Let m represent number of marbles
Let S represent number of Stamps

Kate : Leon
At First:
Marble - 1m : Marble : 0m
Stamps – 0 S : Stamps: 1s

After giving:
Kate : Leon
M --- ½ m : ½ m - 11
S - -- 1/2 s – 5 : ½ S
The ratio of the number of stamps to the number of marbles Keane had left then became 1:7.So,

S / m = 1: 7
1/2s -5 = 1
½ m 7
7/2 S – 35 = ½ m ------------- (1)

ratio of the number of stamps to the number of marbles Leon had left became 1:5

So, s/m = 1 : 5

½ S = 1
½ m – 11 5

5/2 S = 1/2m -11 ------------- (2)
Substituting ½ m from equation (1)

5/2 S = 7/2S-35 – 11
S = 46
Stamps bought by Leon is 46.