Tutor MathsGuru: Ask me for your burning Maths questions!

[Almighty]

Dharma:

Herbie:

Hi Herbie,

The question is telling us when Sam and Ruth meet, they are 30km away from the mid-point of Town A and Town B

You have considered distance as fixed (From Town and Town B) and you found the time and speed ratios but you cannot mix speed/time with distance in an addition/subtraction equation.

The 30km given is DISTANCE ….you cannot subtract time /speed between Sam and Ruth and equate it to distance.

You need to understand what the qn is asking us and apply the appropriate ratio to solve the question.

The question is about meeting of 2 persons. For meeting questions; we know time taken is the same IF both departed at the same time. (Time is constant)

We know the time ratio …. But we need to find the distance ratio. REASON : Qn gives us the difference in distance travelled by Sam and Ruth. (i.e. 30km)

Even my teacher never explains like you Dharma. Thankyou very much Dharma. Thankyou Herbie for posting such questions.

[Dharma]

Herbie:

I have another speed qn.

Rose and Stella travelled from Town A to Town B along the same road but at different speeds.
Rose started her journey 45 min earlier than Stella but Stella reached Town B 20 minutes earlier.

When Stella reached Town B, Rose had travelled 7/8 of the journey and was 25 km away from Town B.
If Rose and Stella travelled at a constant speed.

a. What is the distance btw TOwn A and B? is the ans 175km?
b. What speed was Rose travelling at?
c. How long did Stella take to travel from Town A to Town B.


Tx

a)\t1/8 of the journey => 25km
8/8 of the journey => 25km x 8 = 200km (Distance between Town A and B)

b)\tRose will cover the last 25km of her journey in 20 mins
20 mins => 25km
60 mins => 75km
Rose’s speed = 75km/h

c)\tTime taken by Rose => 20 x 8 = 160 mins
Rose started 45 mins earlier and ended 20 mins later. Therefore, Stella took 65 mins lesser than Rose to complete her journey.
Time taken by Stella = 160 mins – 65 mins = 95 mins

[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 ratio of distance covered is directly proportional or the same as the ratio of the individual’s speed

eg.
Speed : Speed (S)
2 : 3

Time : 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!

[Jolyn]

Hi Guru


I have a few questions which needs your help:

1. Tom is 32kg heavier than Amy. If their total mass is 112kg. How heavy is Amy?

2. A ball of string was cut into 7 equal pieces. Each piece was 50cm long How much string would be left if 2 such peices were given away?

3.A watering can contained 890 ml of water. Angie used 230ml of it to water her carnation plants and 380ml of it to water her rose plants. How much water was left in her watering can?

4. Don bought 12 pineapples and 6 watermelons. How much heavier than the watermelons are the pineapples?

5. Rope A is 17m long. Rope B is thrice as long as Rope A. Rope C is 15m shorter than Rope B. What is the length of Rope C?

Thks

[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?

[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