Tutor MathsGuru: Ask me for your burning Maths questions!

[livewith_vanilla]

MOE Hater:

livewith_vanilla:

Here is a question I would like some help in.


Source: School paper
Level: P6

A train traveled through a 6500-metre tunnel at an average speed of 25m/s. The whole train took 4 min 30 s to pass through the tunnel completely.
What is the length of the train?

TIA.

25m/s x 4 min 30 s = 25m/s x 270s = 6750m
6750m - 6500m = 250m

The train is 250m long.

Thanks too MOE Hater!

[mathsguru]

Almighty:

Hi All,


The figure below, not drawn to scale, is made up of a circle and 3 identical equilateral triangles. The circle has a radius of 14 cm. Find the perimeter of the shaded parts. Take ^(pie) = 22/7

http://www.postimage.org/image.php?v=Tso6CVr
My Method :
Straight line of a shaded portion is the diameter of that semi circle.
Diameter of the shaded arc = 14cm.So,
Circumference of one shaded semicircle = ( 1/2 ^ D) = 1/2 X 22/7 X14
= 22 cm
22 + 14 = 36 cm (Perimeter of one shaded portion).
So, Total perimeter of the shaded portion = 3 X 36 = 108 Cm

Book method :
Combined all the three arcs together so as to form
curved lenght of shaded parts = curved lenght of semi circle.
Ans: 86cm

MY QUESTION:
Can anyone let me know whats wrong in my method were i assumed each shaded portion as a semicircle with diameter 14cm and not 28 cm.
Hope i am clear !! If not pls let me know. Will TRY to reform the question.

Hi Almighty,

Here's my solution for your reference. The diameter should be 28cm.


MathsGuru

http://www.postimage.org/image.php?v=Pq2vyKJ

[mathsguru]

YLH88:

Hi Mathsguru and all,


Need help with the below speed question

A car and a motorcycle set off from Green Town and Pink Town respectively at the same time.
The car, travelling at a constant speed, took 10 hours to reach Pink Town.
The motorcycle, travelling at a constant speed, took 6 hours to reach Green Town.
The vehicles passed by each other when they were 218 3/4 km from Pink Town. Find
a) the distance between the two towns
b) the speed of the car.

Thank you so much!!

Hi YLH88,

Here's my solution! Funny though...that the car travels so much slower than the motorcycle...

Cheers,
MathsGuru

http://www.postimage.org/image.php?v=Tsp4rcS

[mathsguru]

yeodo:

Pls help :


Teck Ming has 30% more stamps than Ravi. Sally has 20% fewer stamps than Ravi. If Teck Ming has 150 stamps than Sally, how many stamps do the three of them have altogether?

Hi Yeodo,

Here's my solution!

Cheers,
MathsGuru

http://www.postimage.org/image.php?v=gxz6sE0

[YLH88]

Hi Mathsguru,


Thank you for the solution. But need to ask : why is it the distance ratio is also 3:5 given the same travelling time ? In the question, the travelling time for car is 10 hours and motorcycle is 6 hrs, so I thought travelling time is different ?

Thank you.

[CoffeeCat]

YLH88:

Hi Mathsguru,


Thank you for the solution. But need to ask : why is it the distance ratio is also 3:5 given the same travelling time ? In the question, the travelling time for car is 10 hours and motorcycle is 6 hrs, so I thought travelling time is different ?

Thank you.

the distance ratio is implying that when in the same amount of time, the distance covered is in the same ratio as that of speed. (in the same time one with higher speed will cover more distance.)
as stated in the solution the same amount of time has passed for both, and the motorcycle will need to cover more distance so that it can finish it's journey faster in less time .

[YLH88]

[quote]YLH88 wrote:

Hi Mathsguru,

Thank you for the solution. But need to ask : why is it the distance ratio is also 3:5 given the same travelling time ? In the question, the travelling time for car is 10 hours and motorcycle is 6 hrs, so I thought travelling time is different ?

Thank you.

Coffeecat wrote :
the distance ratio is implying that when in the same amount of time, the distance covered is in the same ratio as that of speed. (in the same time one with higher speed will cover more distance.)
as stated in the solution the same amount of time has passed for both, and the motorcycle will need to cover more distance so that it can finish it's journey faster in less time .[/quote]Hi Coffeecat,

Thank you for the explanation. But I still don't quite get it. Can I say the first thing is to find the time taken to travel 218 3/4 km from Pink Town for the motorcycle ? If 5u = 218 3/4, can I say 3u = 218 3/4 too ?

Sorry, still blur ... :?

[mathsguru]

YLH88:

[quote]YLH88 wrote:

Hi Mathsguru,

Thank you for the solution. But need to ask : why is it the distance ratio is also 3:5 given the same travelling time ? In the question, the travelling time for car is 10 hours and motorcycle is 6 hrs, so I thought travelling time is different ?

Thank you.

Coffeecat wrote :
the distance ratio is implying that when in the same amount of time, the distance covered is in the same ratio as that of speed. (in the same time one with higher speed will cover more distance.)
as stated in the solution the same amount of time has passed for both, and the motorcycle will need to cover more distance so that it can finish it's journey faster in less time .

Hi Coffeecat,

Thank you for the explanation. But I still don't quite get it. Can I say the first thing is to find the time taken to travel 218 3/4 km from Pink Town for the motorcycle ? If 5u = 218 3/4, can I say 3u = 218 3/4 too ?

Sorry, still blur ... :?[/quote]Hi YLH88,

Given the same travelling time, the vehicle with the faster speed will cover a further distance compared to another vehicle with a slower speed. This difference in distance covered is proportional to their respective speeds. For instance, if I'm driving 2 times your speed, in 1 hr I would have covered twice the distance u covered. Ratio = 2 : 1 --> for both distance and speed, given same travelling time.

Think your confusion here is why is there \"same\" travelling time rite? We must bear in mind that both of them are travelling towards each other and for them to pass each other, they have to be at the same place at the same time. Since they both departed each town at the same time, they would have travelled for the same duration of time by the time they pass each other.

Another point to note is that, the sum of their individual distances covered would amount to the total distance between the 2 towns. Therefore, using their distance ratio of 3 : 5, we can take it as the distance between both towns is a total of 3 + 5 = 8 units. The reason why I took 5 units = 218.3/4km is because 218.3/4km is the distance from Pink town to the point where they meet. This is the distance covered by the motorcycle, not the car. As such, I use 5 units and not 3 units.

Hope this clarifies...Let me know if you're still blur blur...

Cheers,
MathsGuru

p/s: Thanks to Coffeecat for helping me explain! :salute:

[YLH88]

mathsguru:

YLH88:

[quote]YLH88 wrote:

Hi Mathsguru,

Thank you for the solution. But need to ask : why is it the distance ratio is also 3:5 given the same travelling time ? In the question, the travelling time for car is 10 hours and motorcycle is 6 hrs, so I thought travelling time is different ?

Thank you.

Coffeecat wrote :
the distance ratio is implying that when in the same amount of time, the distance covered is in the same ratio as that of speed. (in the same time one with higher speed will cover more distance.)
as stated in the solution the same amount of time has passed for both, and the motorcycle will need to cover more distance so that it can finish it's journey faster in less time .

Hi Coffeecat,

Thank you for the explanation. But I still don't quite get it. Can I say the first thing is to find the time taken to travel 218 3/4 km from Pink Town for the motorcycle ? If 5u = 218 3/4, can I say 3u = 218 3/4 too ?

Sorry, still blur ... :?

Hi YLH88,

Given the same travelling time, the vehicle with the faster speed will cover a further distance compared to another vehicle with a slower speed. This difference in distance covered is proportional to their respective speeds. For instance, if I'm driving 2 times your speed, in 1 hr I would have covered twice the distance u covered. Ratio = 2 : 1 --> for both distance and speed, given same travelling time.

Think your confusion here is why is there \"same\" travelling time rite? We must bear in mind that both of them are travelling towards each other and for them to pass each other, they have to be at the same place at the same time. Since they both departed each town at the same time, they would have travelled for the same duration of time by the time they pass each other.

Another point to note is that, the sum of their individual distances covered would amount to the total distance between the 2 towns. Therefore, using their distance ratio of 3 : 5, we can take it as the distance between both towns is a total of 3 + 5 = 8 units. The reason why I took 5 units = 218.3/4km is because 218.3/4km is the distance from Pink town to the point where they meet. This is the distance covered by the motorcycle, not the car. As such, I use 5 units and not 3 units.

Hope this clarifies...Let me know if you're still blur blur...

Cheers,
MathsGuru

p/s: Thanks to Coffeecat for helping me explain! :salute:[/quote]Hi Mathsguru,

What I don't understand is that I thought distance and speed will be in the same ratio if the time is constant, but in this question,
a) time for car is 10 hr and time for motorcycle is 6 hr, and
b) the 5u for the time for motorcycle isn't it for the whole journey ? how come is 5u = 218 3/4 ??

very sorry, still can't see the picture

[Dharma]

YLH88:

mathsguru:

[quote=\"YLH88\"]
Hi Coffeecat,

Thank you for the explanation. But I still don't quite get it. Can I say the first thing is to find the time taken to travel 218 3/4 km from Pink Town for the motorcycle ? If 5u = 218 3/4, can I say 3u = 218 3/4 too ?

Sorry, still blur ... :?

Hi YLH88,

Given the same travelling time, the vehicle with the faster speed will cover a further distance compared to another vehicle with a slower speed. This difference in distance covered is proportional to their respective speeds. For instance, if I'm driving 2 times your speed, in 1 hr I would have covered twice the distance u covered. Ratio = 2 : 1 --> for both distance and speed, given same travelling time.

Think your confusion here is why is there \"same\" travelling time rite? We must bear in mind that both of them are travelling towards each other and for them to pass each other, they have to be at the same place at the same time. Since they both departed each town at the same time, they would have travelled for the same duration of time by the time they pass each other.

Another point to note is that, the sum of their individual distances covered would amount to the total distance between the 2 towns. Therefore, using their distance ratio of 3 : 5, we can take it as the distance between both towns is a total of 3 + 5 = 8 units. The reason why I took 5 units = 218.3/4km is because 218.3/4km is the distance from Pink town to the point where they meet. This is the distance covered by the motorcycle, not the car. As such, I use 5 units and not 3 units.

Hope this clarifies...Let me know if you're still blur blur...

Cheers,
MathsGuru

p/s: Thanks to Coffeecat for helping me explain! :salute:

Hi Mathsguru,

What I don't understand is that I thought distance and speed will be in the same ratio if the time is constant, but in this question,
a) time for car is 10 hr and time for motorcycle is 6 hr, and
b) the 5u for the time for motorcycle isn't it for the whole journey ? how come is 5u = 218 3/4 ??

very sorry, still can't see the picture :([/quote]Hi YLH88,

There are 2 steps to this question. We are given the time taken by the car and motorcycle to travel the same distance ( between Green Town and Pink Town) which are 10 hrs and 6 hrs respectively.

Step 1
When the 2 vehicles travel the same distance (Green Town to Pink Town for the car and Pink Town to Green Town for the motorcycle); the distance is constant.

We find the speed ratio from the time ratio
Speed ratio => Car : Motorcycle = 3 : 5

Step 2
We are also told that when the car and motorcycle pass each other (because they travelled in opposite direction and started at same time); the distance that the motorcycle travelled was 218.75km when it passed the car.

We know that when 2 vehicles started at the same time and are moving towards each other, the time taken when the pass by each other is the same for both vehicles.

At the point where the car and motorcycle pass by each other, time is constant.

Distance ratio (Car : Motorcycle) = Speed ratio (Car : Motorcycle) = 3 : 5

5u = 218.75km (motorcycle travelled 5u to meet the car and 5u is 218.75km)
8u = 350km (Distance between Green Town and Pink Town)

Speed of car = 8u / 10hrs = 350km / 10hrs = 35km/h