Tutor MathsGuru: Ask me for your burning Maths questions!

[Dharma]

firebird:

Dear mathsguru


Good morning

Please help me on the following P6 Speed math:

A Van left Port Penang for Town Lalu at 9 a.m. A Car started its journey along the same route as the Van from starting point, two hours later. The car overtook the Van at 3 p.m. The speed of the car was 30 Km/h higher than Van. The Van took 7 hours to reach Town Lalu. Find the distance between Port Penang and Town Lalu.

The answer given was:

a) The speed of the car was 30 km/h more than the speed of the Van.
So 1hr = 30 km
4hr = 4 X 30 = 120 Km

I can understand this. Reason is 4 hours = (11am - 3 pm)


b) Distance travelled from Port Penang to Town Lalu
2 hours = 120 Km
7 hours = 120/2 X 7 = 420 Km (which is the answer given)

I really do not understand how 2 hours is linked to 120 km

Please help me as to how 2 hours is linked to 120 km.
Are there different method/steps / explaination available?

Thank you
Firebird

For fixed distance (from Port Penang to the point where car overtakes van);

Time ratio => Van: Car = 3:2 (van takes 6 hrs and car takes 4 hrs)
Speed ratio => Van: Car = 2:3

3u – 2u = 30
Speed of van = 60km/h

Distance between Port Penang & Town Lalu = 60km/h x 7hrs = 420km

[firebird]

Dear Dharma


I fully understand now.

Thank you very much.

With best regard
Firebird

[Almighty]

Thankyou very much coffee cat…I also had the same querry for the speed problem…I will assume in the same way as gn by you.Thankyou very much again.

[MOE Hater]

Hiya folks,


Went APMOPS a while back and this was one of the questions. i think the answer is 15 but if u guys get something higher, i would be happy to know. Here's the question:

what is the largest possible remainder when a 2-digit number was divided by it's digit sum?

Note: the digit sum can be a 2-digit number, it does not have to be a 1-digit number. For example, the digit sum of 99 is 18, you do not have to find the digit sum till it is a single digit number(i.e.9).

Thanks in advance :?:

[abc_parent]

Will anyone have the exam paper and help me to answer Q13b, Q14, Q15? These are questions to do with Circles and I really cannot solve. But I cannot upload pic. Will try to figure out when I really have the time!!!


But if you don’t have, can help me with this question?
Container A contains 250 red marbles and 200 blue marbles.
Container B contains 600 red marbles and 150 blue marbles.
How many red and blue marbles must be moved form Container A to Container B such that 25% of the marbles in Container A are red and 75% of the marbles in Container B are red?

Ans: 350 - Can explain step by step? Thanks!

[CoffeeCat]

MOE Hater:

Hiya folks,


Went APMOPS a while back and this was one of the questions. i think the answer is 15 but if u guys get something higher, i would be happy to know. Here's the question:

what is the largest possible remainder when a 2-digit number was divided by it's digit sum?

Note: the digit sum can be a 2-digit number, it does not have to be a 1-digit number. For example, the digit sum of 99 is 18, you do not have to find the digit sum till it is a single digit number(i.e.9).

Thanks in advance :?:

yea your answer is right. Any other interesting questions to share?

[MOE Hater]

abc_parent:

Will anyone have the exam paper and help me to answer Q13b, Q14, Q15? These are questions to do with Circles and I really cannot solve. But I cannot upload pic. Will try to figure out when I really have the time!!!


But if you don't have, can help me with this question?
Container A contains 250 red marbles and 200 blue marbles.
Container B contains 600 red marbles and 150 blue marbles.
How many red and blue marbles must be moved form Container A to Container B such that 25% of the marbles in Container A are red and 75% of the marbles in Container B are red?

Ans: 350 - Can explain step by step? Thanks!

This is actually a basic olympiad problem if i am not mistaken. It can be solved with basic algebra requiring 5-6 steps.

Let a be the number of marbles in Container A in the end and let b be the number of marbles in Container B in the end

We can find that 1/4 a + 3/4 b is the total number of red marbles and that 3/4 a + 1/4 b is the total number of blue marbles. So,

1. 1/4 a + 3/4 b = 600 + 250 = 850
2. 3/4 a + 1/4 b = 200 + 150 = 350

To solve such a problem, which is called Simultaneous Equations by the way, we can try to make one of the values common to both equations so that we can find the value of the other variable. In this case, we can make the value of a in both equations 3/4.

As 3/4 a / 1/4 a = 3, we have to multiply the entire equation 1 by 3. So,

(1/4 a + 3/4 b) x 3 = 850 x 3
3/4 a + 9/4 b = 2550

We can then subtract the above equation with the 2nd equation so that the variable a is cancelled out.

3/4 a + 9/4 b - 3/4 a + 1/4b = 2550 - 350 8/4 b = 2b = 2200
b = 1100

By adding equation one and two we can get the total value of a and b.

1/4 a + 3/4 b + 3/4 a + 1/4 b = 850 + 350
a + b = 1200
a = 100

Marbles in Container A at first = 250 + 200 = 450

Marbles removed from Container A = 450 - 100 = 350

P.S. Sorry about Skpe action, can't remove it

[YLH88]

[quote]
Mr F drove from home to work at 60km/h . After work, he needed to rush home for dinner and increased his speed on his way home by 30 km/h. As a result, he tool 5 minutes less than what he had taken on his way to work. What was the distance between his house and office?

Ans given: 15km

Distance between his house and office is fixed, Speed is inversely proportional to the time taken.
Speed ratio = 2 : 3
Time ratio = 3 : 2
3u – 2u = 1u = 5/60 = 1/12 hrs (Difference in time taken)

Distance = 60km/h x 3 x 1/12hrs = 15km[/quote]Hi Dharma,

Would like to check for Speed questions, is the inversely proportional concept always apply to Speed and Time ? why is that so har ? I am not sure when to use this inversely proportional concept and for only Speed and Time ? can it be use for distance and time or distance and speed ?

Sorry, I don't really know how to apply this inversely proportional concept in Speed questions so can't explain clearly to my DS. :?

[CoffeeCat]

MOE Hater:

abc_parent:

Will anyone have the exam paper and help me to answer Q13b, Q14, Q15? These are questions to do with Circles and I really cannot solve. But I cannot upload pic. Will try to figure out when I really have the time!!!


But if you don't have, can help me with this question?
Container A contains 250 red marbles and 200 blue marbles.
Container B contains 600 red marbles and 150 blue marbles.
How many red and blue marbles must be moved form Container A to Container B such that 25% of the marbles in Container A are red and 75% of the marbles in Container B are red?

Ans: 350 - Can explain step by step? Thanks!

This is actually a basic olympiad problem if i am not mistaken. It can be solved with basic algebra requiring 5-6 steps.

On the contrary, this is a challenging problem sum and unlikely to appear in any maths olympiad other than nmos (even so it has probably not appeared in nmos yet).

[Dharma]

YLH88:

[quote]
Mr F drove from home to work at 60km/h . After work, he needed to rush home for dinner and increased his speed on his way home by 30 km/h. As a result, he tool 5 minutes less than what he had taken on his way to work. What was the distance between his house and office?

Ans given: 15km

Distance between his house and office is fixed, Speed is inversely proportional to the time taken.
Speed ratio = 2 : 3
Time ratio = 3 : 2
3u – 2u = 1u = 5/60 = 1/12 hrs (Difference in time taken)

Distance = 60km/h x 3 x 1/12hrs = 15km

Hi Dharma,

Would like to check for Speed questions, is the inversely proportional concept always apply to Speed and Time ? why is that so har ? I am not sure when to use this inversely proportional concept and for only Speed and Time ? can it be use for distance and time or distance and speed ?

Sorry, I don't really know how to apply this inversely proportional concept in Speed questions so can't explain clearly to my DS. :?[/quote]
Hi YLH88,

For speed questions, we know Distance = Speed x Time

So, for constant/fixed distance (i.e. 2 vehicles travelling the same distance but having different speeds); the time taken by the faster vehicle will be shorter and the slower vehicle will take a longer time for the same distance.
So, if the distance is constant, then we can say that speed and time are inversely proportional.

Now, for constant time (time taken by 2 vehicles is the same), we can say that the faster vehicle will travel a longer distance compared to a slower vehicle.
Here, if the time is constant, we say the speed and distance travelled by a vehicle is directly proportional.

For 2 vehicles having constant speed, the vehicle that travels a longer distance will take a longer time.
So, for constant speed, the distance travelled by a vehicle is directly proportional to the time taken.

The ratio method can be applied for speed questions but u need to determine which one (either speed, time or distance is fixed) from the question.

From the concept above, see whether u can understand & explain the question above to you son.