Tutor MathsGuru: Ask me for your burning Maths questions!

[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

[Budo]

Hi need help in this question


Andrew and Brian had some money
If Andrew gave Brian $55, the ratio of Andrew to Brian amount is 3:5.
If Brian gave Andrew 20% of this money and $10, Andrew would have $108 more than Brian.
How much do Andrew and Brian have at first?

:?

[Almighty]

Dharma:

Almighty:

[quote]
Radius of the circle = 14cm. So, diameter of circle = 28cm

You had used diameter as 14cm instead of 28cm in your computation of circumference of the semi circle.

[/quote]Thankyou Dharma and math guru

[Almighty]

Almighty:

Almighty:

Question :5Pattern II -photo print


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

Hi MAthmonster,Dharma,Ksi & others......
Reposting...If this qt had missed yr eye...Since i posted many qt last night.
Pl.try to help me on this too..

Hi MathGuru,

This question of mine is still unanswered.Can you help?

[YLH88]

Dharma:

YLH88:

[quote=\"mathsguru\"]
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

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[/quote]Hi Mathsguru, Coffeecat, Dharma,

Thank you very much for all the explanation. Now I get it. at first, I kept wondering how come 5u = 218 3/4, keep thinking 5u is the total distance between the 2 towns.

[super star]

Maths guru

please help me in this problem.

Alan,Ben&charles had 864 trading cards.Ben won some of the cards from alan &as a result,ben’s cards increased by 50%.charles then won some cards from ben & charles’cards increased by 40%.finally charles lost some of his cards to alan & alan’s cards increased by 20%.In the end ,they realised that they each had an equal number of cards.how many cards did alan have at first?

[mathsguru]

Budo:

Hi need help in this question


Andrew and Brian had some money
If Andrew gave Brian $55, the ratio of Andrew to Brian amount is 3:5.
If Brian gave Andrew 20% of this money and $10, Andrew would have $108 more than Brian.
How much do Andrew and Brian have at first?

:?

Hi Budo,

Here's my solution. Hope it helps!


MathsGuru

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

[mathsguru]

YLH88:

Hi Mathsguru, Coffeecat, Dharma,


Thank you very much for all the explanation. Now I get it. at first, I kept wondering how come 5u = 218 3/4, keep thinking 5u is the total distance between the 2 towns.

That's great! Glad that you understand it now...

Cheers,
MathsGuru

[mathsguru]

super star:

Maths guru

please help me in this problem.

Alan,Ben&charles had 864 trading cards.Ben won some of the cards from alan &as a result,ben's cards increased by 50%.charles then won some cards from ben & charles'cards increased by 40%.finally charles lost some of his cards to alan & alan's cards increased by 20%.In the end ,they realised that they each had an equal number of cards.how many cards did alan have at first?

Hi Super Star,

This question was posted quite some time back by another forum member. Here's my solution anyway...trick here is to work backwards systematically.

Cheers,
MathsGuru

http://www.postimage.org/image.php?v=gxHh7s0