Tutor MathsGuru: Ask me for your burning Maths questions!

[Dharma]

Almighty:

Maths Monster:

[quote=\"Almighty\"]Question :8 - speed -EDITED

Tom, Bob and Kel;vin started running at the same point X at the same time round a circular track. Tom ran in a clockwise direction but Bob and Kelvin ran in an anti-clockwise direction. Tom took 7 minutes to complete each round. He met Bob after every 4 minutes and he met Kelvin after every 2 minutes. Each of them ran at the same uniform speed throughout.
a) What was the ratio of Toms speed to Kelvin's speed to Bob's speed?Ans:4:10:3.
b) When Tom and Bob met again at X after 21 minutes, Tom had already run 4200m. What was the distance ran by Kelvin when Tom met Bob at X after 21 minutes?
section B cannot understand the method.pl.brief.Ans:3500m

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

Tom ran 1 round in 7 mins. His speed is 1/7 round per min.

In 2 mins, he ran 2/7 round.
In the same time, Kelvin ran 5/7 round to meet Tom
Kelvin speed is 5/7 / 2 = 5/14 round per min.

In 4 mins, he ran 4/7 round.
In the same time, Bob ran 3/7 round to meet Tom
Bob speed is 3/7 / 4 = 3/28 round per min.

a) Ratio of speed:
Tom : Kelvin : Bob
1/7 : 5/14 : 3/28
4 : 10 : 3

b) Tom and Bob meet every 4 mins, ie in the multiply of 4.
21 / 4 = 5.25, therefore we use 6x4 = 24 mins
After 24 mins, Tom ran 24/7 rounds = 4200m
Each round = 4200 x 7/24 = 1225m

Therefore, in 24 mins, Kelvin ran 5/14 x 24 x 1225 = 10,500m

Hi mathsmonster.The answer for section b is different from the one gn in the answerkey:It states the follw:
21 min = 4200m
7min = 4200/21x7
1 round = 1400m
Kelvin completed 2.5 rounds in 7 min, so, 2.5 x 1400 = 3500m.(ANS)
I dint understand the part writted in red. Pl.explain.Sorry 2 trouble u again..[/quote]a)

Time ratio
Tom : Bob = (7 – 4) : 4 = 3 : 4
Tom : Kelvin = (7 – 2) : 2 = 5 : 2
Tom : Kelvin : Bob = 15 : 6 : 20

Speed ratio
Tom : Kelvin : Bob = 1/15 : 1/6 : 1/20 = 4/60 : 10/60 : 3/60 = 4 : 10 : 3

b)

In 21 mins; Tom completed 3 rounds
1 round = 4200m/3 = 1400m
If time is constant
Distance ratio => Tom : Kelvin : Bob = 4 : 10 : 3
4u = 4200
1u = 1050m

After 21 mins; Kelvin had run 10u (10 x 1050m) = 10500m.

# The part in red is given in the qn. Tom takes 7 mins to complete 1 round. So, in 21 mins he would have completed 3 rounds which is 4200m.

From distance ratio we know that in the same time, Tom travels 4u Kelvin would have covered 10u (Kelvin's speed is 2.5 times Tom's speed)

If Kelvin completes 1400m x 2.5 = 3500m in 7 mins.
He will complete 3500m x 3 = 10,500m in 21 mins.

I agree with MM's answer.

[liketoeat]

Tang:

Dharma:

[quote=\"Vanilla Cake\"]
Since this is a P6 question then use algebra which is good enough to solve and gain full marks.
Let number of cubes added be n
( 5x1.58 )+( nx1.6 )=( n+5 )x1.595
n=15
Number of cubes added = 15

Hope other members will forward with non-algebraic approach so that readers of this forum can learn.

http://www.postimage.org/image.php?v=aVb175J

Increase in average --> 1.595 - 1.58 = 0.015

Total increase --> 0.015 x 5 = 0.075 kg

Decrease in average --> 1.600 - 1.595 = 0.005

So number of cubes added --> 0.075/0.005 = 15 cubes

15 cubes were added.[/quote]Thank you all for the solutions.

[Hifive]

Hi Vanilla Cake


Thanks for the help with my question.

[Almighty]

Maths Monster:

For part (b), I may have assumed wrongly that Tom and Bob meet at 24 mins. But the fact is that Tom and Bob does not meet at 21 mins. They meet every 4 mins, ie multiply of 4.

As for the answer given, the distant that Kelvin ran is for 7 mins which seems to contradict the question which states after 21 mins.

Based on the two points above, I am not sure if the question is correctly stated. Perhaps, you can check again on the question to verify it is correct. BTW, where is this question taken from?

Cheers,
MM

Thank you for yr detailed explanation MM.Its from
Andrew ER's Worksheet P6 Assessment book Editioon 2009.I also went wrong in tht step n dint know how is \" the distant that Kelvin ran is for 7 mins which seems to contradict the question which states after 21 mins.\"

[newbieparent]

:?: Hi Maths Guru, Need some help with the following questions:


1) ACS 2009 P6 Prelim Paper 2 Q10

2) Henry Park 2009 P6 Prelim Paper 2 Q15

3) Nanyang Pri 2009 P6 Prelim Paper 2 Q14

4) Catholic High 2009 P6 Prelim Paper 1 Q13

Anyone who can help? Will be very grateful!

[Herbie]

Hi Dharma,


Sorry, I have to come back to the speed related issues.

Would u be able to reiterate the inverse formula for speed as indicated below:

Constant distance
Ratio of speed is inversely proportional to the ratio of time

Constant speed
Ratio of distance is directly proportional to the ratio of time

Constant time
Ratio of distance is directly proportional to the ratio of speed



I can’t locate yr previous explanantion.

So sorry!

many thanks!

[Dharma]

Herbie:

Hi Dharma,


Sorry, I have to come back to the speed related issues.

Would u be able to reiterate the inverse formula for speed as indicated below:

Constant distance
Ratio of speed is inversely proportional to the ratio of time

Constant speed
Ratio of distance is directly proportional to the ratio of time

Constant time
Ratio of distance is directly proportional to the ratio of speed.

I can't locate yr previous explanantion. :-

So sorry!

many thanks!

Hi Herbie,

For speed, we need to know that distance = speed x time.
We know that if distance is fixed; then speed and time are inversely proportional to each other.

For speed questions, we normally deal with at least 2 moving objects (car, bus,lorry or even 2 or more persons running or walking) either in the same direction or opposite directions.

Therefore, when we have 2 or more moving objects, we try to find out the speed ratio or time ratio if the 2 objects. In this case the. 2 objects must be travelling the same distance, so distance is fixed or constant. This being the case, then the speed ratio of the 2 objects (if given) can be used to find the time ratio of the 2 objects ;because they are inversely proportional to each other. In the same way, if we know the time ratio of the 2 objects we can proceed to find out their speed ratio.

Hope u are able to understand.

[Mathematically Speaking]

MathGuru,


what software do you use to draw all your models? I am truly impressed! Perhaps the teachers in school should start doing this…

[Herbie]

Hi Dharrna,


Thanks for yr reply.

Many thanks!

[liketoeat]

Hi, please help me solve this question. Thank you.


Candle A and candle B were placed on a table. Candle A was 1.5 cm longer than candle B. Candle A and candle B were lighted at 0630 h and 0800 h respectively. They burnt down to the same length at 1030 h. At 1200 h, candle B was burnt out while A only burnt out at 1230 h. Given that the rate of burning of each candle was constant throughout, find the original length of each candle. (Ans: candle A 13.5 cm; candle B 12 cm)