Tutor MathsGuru: Ask me for your burning Maths questions!

[Herbie]

Hi Dharma can help with the speed qn below:


A van travelled from town A to town B at an average spped of 55km/h. A car started its journey from Town B to town A at the same time as the van, travelling at an average speed of 90km/h. The two vehicles passed each other 70km from the middle of the whole journey. Find the distance between the two towns.

TIA

[Dharma]

Herbie:

Hi Dharma can help with the speed qn below:


A van travelled from town A to town B at an average spped of 55km/h. A car started its journey from Town B to town A at the same time as the van, travelling at an average speed of 90km/h. The two vehicles passed each other 70km from the middle of the whole journey. Find the distance between the two towns.

TIA

Speed ratio => Van : Car = 11 : 18

When time is fixed ( when they meet)

Distance ratio => Van : Car = 11 : 18
18u - 11u = 7u
7u = 70km x 2 = 140km
1u = 20km
Distance betwen the towns = 29u = 29 x 20km =580km

[Vanilla Cake]

Herbie:

I have 2 qns,

Hi Herbie,
While waiting for Uncle Dharma's solutions, pls see whether my solutions are of any help or not?
Thks.

Herbie:

a. For every $2 that Edyy spent, Fred spent $3. After Eddy had spent all his money. Fred still had 3/8 of the total amount of the two boys had at first.
What fraction of the total amount of money did Eddy have at first?
What was the ratio of Fred's money to Eddy's money at first?

This is a 5-mark question from Rulang Primary School P6 Prelim 2009 paper 2 Q17

E: [s][s]
F: [s][s][s][][][]

Note: [s]-Money spent.

2/8=1/4
(a) Fraction of the total amount of money that Eddy had at first = 1/4.

From the model drawing:
6:2
3:1
(b) Ratio of Fred's money to Eddy's money at first = 3:1

Herbie:

b. Mr Lee Left Town M and travelled towards Town N at an average speed of 80km/h. An hour later, mr ong left Town M and travelled towards Town N at an average speed of 100km/h. mr Ong passed Town Q which was halfway between Town M and Town N 30 minutes earlier than Mr Lee. If Mr Ng reached Town N at 10pm, at what time did Mr Lee leave Town M for Town N?

This is a 4-mark question from Rulang Primary School P6 Prelim 2009 paper 2 Q11
From Town M to Town Q, Mr Ong took 1 h+1/2h = 1 and 1/2 h less time than Mr Lee.
Since Town Q was the mid-point, Mr Ong took 1.5 hx2 = 3 h less time than Mr Lee to travel from Town M to Town N.

Ratio of speed
Mr Ong : Mr Lee
100 : 80
5 : 4

Ratio of time
Mr Ong : Mr Lee
4 : 5

Difference in the ratio of time = (5-4)units = 1 unit -> 3 hours
Mr Ong took 4 units which was equal to 4x3 hours = 12 hours
Since Mr Ong reached Town N at 10 p.m., he left Town M at 10 a.m.
So, Mr Lee Left Town M at 9 a.m. for Town N.

[Dharma]

Herbie:

I have 2 qns,


a. For every $2 that Edyy spent, Fred spent $3. After Eddy had spent all his money. Fred still had 3/8 of the total amount of the two boys had at first.

What fraction of the total amount of money did Eddy have at first?
What was the ratio of Fred's money to Eddy's money at first?

b. Mr Lee Left Town M and travelled towards Town N at an average speed of 80km/h. An hour later, mr ong left Town M and travelled towards Town N at an average speed of 100km/h. mr Ong passed Town Q which was halfway between Town M and Town N 30 minutes earlier than Mr Lee. If Mr Ng reached Town N at 10pm, at what time did Mr Lee leave Town M for Town N?


TIA.

Q1
The amount of money Eddy and Fred had at first ( N = no. of days Eddy to spend all his money)
Eddy : $2N
Fred : $3N + $3N = $6N ( $3N is the amount Fred had left; so fraction Fred had left = 3/(6 + 2) = 3/8 )

a)\tFraction of total amt Eddy had at first = 2/ (2 + 6) = ¼
b)\tRatio = 6 : 2 = 3: 1

Q2
When Ong left Town M, Lee had already travelled 80km (80km/h x 1 hr)
Time taken to overtake = 80km/(100km/hr – 80km/hr) = 4 hrs
From overtaking point to the midpoint of both towns; distance is constant(fixed)

Speed ratio => Lee : Ong = 4 : 5
Time ratio => Lee : Ong = 5 : 4
5u – 4u = 1u = ½ hr
Time taken by Ong = 4u = 2 hrs
Time taken by Ong to travel from Town M to Town N = (4 + 2)hrs x 2 = 12 hrs
Ong left Town M at 10am (12 hrs before 10pm)
So, Lee left Town M at 9am (1 hr before Ong)

[maths6a]

Dear Gurus out there, need help with 2 questions:-


1. If Andy runs up 7 steps of the escalator, he will take 36 sec to reach the top of the escalator. If he runs up 13 steps, he will take him only 27 sec to reach the top. How many seconds would it take him to reach the top if he did not run up any steps of the escalator at all?

2. When asked how many gold coins a miser had, his reply was, " If I divide the coins into 2 unequal numbers, then 49 times the difference between the two numbers equals the difference between the squares of the two numbers."
How many coins did he have?

Thank you in advance fof the solution.

[tianzhu]

Hi maths6a


Just curious, where are your two questions from? They don’t look like questions from past years papers.
[quote]If Andy runs up 7 steps of the escalator, he will take 36 sec to reach the top of the escalator. If he runs up 13 steps, he will take him only 27 sec to reach the top. How many seconds would it take him to reach the top if he did not run up any steps of the escalator at all? [/quote]If Andy runs up 7 steps, he needs 36 seconds to reach the top of the escalator.

If he runs up 13 steps, he needs 27 seconds to reach the top the escalator .

36-27 ----- 9
Therefore each additional step takes 9/6 -------1.5 seconds

Total steps in escalator = 7 + 36 /1.5 ----- 31

or 13 + 27/1.5 ------ 31

If he did not run up any steps, he will take 31*1.5 ------ 46.5 seconds.
[quote]When asked how many gold coins a miser had, his reply was, \" If I divide the coins into 2 unequal numbers, then 49 times the difference between the two numbers equals the difference between the squares of the two numbers.\"
How many coins did he have? [/quote]The second question involves difference of squares formula.

a2 - b2 = (a + b) (a - b) (a2 means a to the power of 2)

Given a2 - b2 = 49(a-b)

Therefore (a+b) (a-b) = 49(a-b)
Hence (a+b) =49

Use listing or GC
Try a=25, b=24
625-576 = 49(25-24)

There are 49 coins

[maths6a]

tianzhu:

Hi maths6a


Just curious, where are your two questions from? They don’t look like questions from past years papers.
[quote]If Andy runs up 7 steps of the escalator, he will take 36 sec to reach the top of the escalator. If he runs up 13 steps, he will take him only 27 sec to reach the top. How many seconds would it take him to reach the top if he did not run up any steps of the escalator at all?

If Andy runs up 7 steps, he needs 36 seconds to reach the top of the escalator.

If he runs up 13 steps, he needs 27 seconds to reach the top the escalator .

36-27 ----- 9
Therefore each additional step takes 9/6 -------1.5 seconds

Total steps in escalator = 7 + 36 /1.5 ----- 31

or 13 + 27/1.5 ------ 31

If he did not run up any steps, he will take 31*1.5 ------ 46.5 seconds.
[quote]When asked how many gold coins a miser had, his reply was, \" If I divide the coins into 2 unequal numbers, then 49 times the difference between the two numbers equals the difference between the squares of the two numbers.\"
How many coins did he have? [/quote]The second question involves difference of squares formula.

a2 - b2 = (a + b) (a - b) (a2 means a to the power of 2)

Given a2 - b2 = 49(a-b)

Therefore (a+b) (a-b) = 49(a-b)
Hence (a+b) =49

Use listing or GC
Try a=25, b=24
625-576 = 49(25-24)

There are 49 coins[/quote]Wow, what kind of questions are these? They are just 2 of the questions in my P4 neighbour's worksheet over the september holidays! Managed to help her with the rest but have no clue how to help her with these 2 so better check with the experts here. Thanks!

[Hiroii-kun]

Dear Gurus,

need help with this question.

At first, warehouse X and Y had a total of 10400 sacks of rice. After warehouse X has cleared 3/4 of its stock and warehouse Y has cleared 3/5 of its stock, warehouse Y now has 520 more sacks of rice than warehouse X. How many sacks of rice did each warehouse have at first?

Ans is 5600 & 4800 but cant seem to get it.

[Dharma]

Hiroii-kun:

Dear Gurus,

need help with this question.

At first, warehouse X and Y had a total of 10400 sacks of rice. After warehouse X has cleared 3/4 of its stock and warehouse Y has cleared 3/5 of its stock, warehouse Y now has 520 more sacks of rice than warehouse X. How many sacks of rice did each warehouse have at first?

Ans is 5600 & 4800 but cant seem to get it.

4u + 5p = 10400 ........ (1)
2p - 1u = 520 ..............(2)
8p - 4u = 2080 .............(2) x 4 = (3)

13p = 12480 ........(1) + (3)
1p = 960
1u = 1400
X => 4u = 4 x 1400 = 5600
Y => 5p = 5 x 960 = 4800

[Hiroii-kun]

Dharma:

Hiroii-kun:

Dear Gurus,

need help with this question.

At first, warehouse X and Y had a total of 10400 sacks of rice. After warehouse X has cleared 3/4 of its stock and warehouse Y has cleared 3/5 of its stock, warehouse Y now has 520 more sacks of rice than warehouse X. How many sacks of rice did each warehouse have at first?

Ans is 5600 & 4800 but cant seem to get it.

4u + 5p = 10400 ........ (1)
2p - 1u = 520 ..............(2)
8p - 4u = 2080 .............(2) x 4 = (3)

13p = 12480 ........(1) + (3)
1p = 960
1u = 1400
X => 4u = 4 x 1400 = 5600
Y => 5p = 5 x 960 = 4800

ooh thanks!