Tutor MathsGuru: Ask me for your burning Maths questions!

[Vanilla Cake]

tiger262:

Cars are travelling to and fro from Greens Town to Sins City. The cars leave the Towns at regular interval and a car will meet another car coming in the opposite direction at every 6 min. Ronald starts cycling from Greens Town to Sins City while Annie starts cycling in the opposite direction. Both leave the Towns at the same time. Ronald and Annie will meet a car coming in the opposite direction every 7 and 8 min respectively. They met each other after cycling for 56 min. What is the time taken by a car to travel from Greens City to Sins City?

tiger262:

This question was asked by my friend's son who is a P6 student. I am sorry that I am unable to locate the source.
I was very impressed with this thread. So many kind people are helping with their time and effort to solve difficult problems. I am sure someone can post a solution with explanations so that a P6 student can understand. Kindly help out. Thanks a lot.

Hi tiger262,
While waiting for someone to post a solution with explanations so that a P6 student can understand, pls refer to solutions from Uncle Observer:

http://psle2010a.blogspot.com/2010/06/speed-p6_22.html dated Tue, 22 June 2010
http://prischoolmaths.blogspot.com/2009/11/speed_30.html dated Mon, 30 Nov 2009.

Dear readers:Take note that this question was already available sometime late last year (2009).

[CoffeeCat]

Uncle Observer is amazing for already posted solutions to many questions asked in this forum and vanilla is amazing for locating them.


For such challenging speed questions it will definitely aids in understanding if you draw the usual distance line thingy.
First I define the car’s speed to be x km/min. Notice that all the cars are a certain distance from each other.
First, from "a car will meet another car coming in the opposite direction at every 6 min", the distance between each car will be 12x km.
From "Ronald and Annie will meet a car coming in the opposite direction every 7 and 8 min respectively.", let’s look at ronald.
Imagine at the 7th min, it has just met a car. now it is going to met the next car in 7 mins. In that 7 mins the car would have covered 7x km. Ronald will have to cover 5x km in 7 mins.
Similarly Annie will have to cover 4x km in 8 mins.

In order to answer the question we need to find the distance in terms of x.
So in 56 mins, Ronald will have covered 85x = 40x km,
and Annie will have covered 74x = 28x km.
Total distance 68x km.
Time taken = 68mins.

[Almighty]

Thank you dharma

[tiger262]

Thank you so much Vanilla Cake for locating the solutions. Your speed in locating them is amazing.


But honestly the solutions could be understood only with the lucid explanations offered by Coffeecat. Thanks to you Coffeecat. Without you, I would still be trying to make sense of Uncle’s solutions.

Coffeecat and Vanilla cake are both phenomenal in their contributions.

[SKT]

Can anyone help:


1. Jerry spent $176 on a tennis racket and 1/7 of the remainder of his money on a book. Then, he bought a calculator for $110. If he had 1/15 of his money left. How much did he have at first?

2. Swee Long, Rafi and Ted share 19 stamps. The ratio of Swee Long’s share to the total number of stamps is 1:5. The ratio of Rafi’s share to the total number of stamps is 1:4. The ratio of Ted’s share to the total number of stamp is 1:2. Find the number of stamps each boy gets. (Hint: None of the stamps are cut)

3. Number of chicken sold was thrice the number of ducks. There were 90 chickens left by the time all the ducks were sold. However if the ducks sold was thrice the number of chicken sold, there would be 330 chickens left by the time all the ducks were sold.
(a) total number of chickens and ducks on farm.
(b)What was the ratio of the number of ducks to the number chickens?

4. There are some apples and pears in a box. If 3 apples are remove, the number of apples will be 1/5 of the total number of fruits left. If 10 pears are removed, the number of apples will be 1/3 of the total number of fruits left. How many pears are there?

[Ngserene617]

Hi kindly assist me for the below 3 stated questions, thanks.


1. Alex, Bryan and Charles paid for a meal. Alex paid 1/5 of the amount Bryan and Charles paid together. Bryan paid 1/4 of the amount Alex and Charles paid. If the meal cost $205.20, how much did Alex pay ?

2. Terry had $420 more than Sean. Sean gave Terry $72. Now, Sean has 1/7 as much money as Terry. How much money had Terry at first?

3. 3 sisters, Amy, Bonnie and Cindy shared to buy a present for their mother. Amy paid 1/3 of the amount which Bonnie and Cindy paid. Bonnie paid 1/5 of the amount which Amy and Cindy paid. If Cindy paid $30 more than Bonnie, how much did the present cost?


Thanks kindly help me to solve this !

[Dharma]

SKT:

Can anyone help:


1. Jerry spent $176 on a tennis racket and 1/7 of the remainder of his money on a book. Then, he bought a calculator for $110. If he had 1/15 of his money left. How much did he have at first?

2. Swee Long, Rafi and Ted share 19 stamps. The ratio of Swee Long's share to the total number of stamps is 1:5. The ratio of Rafi's share to the total number of stamps is 1:4. The ratio of Ted's share to the total number of stamp is 1:2. Find the number of stamps each boy gets. (Hint: None of the stamps are cut)

3. Number of chicken sold was thrice the number of ducks. There were 90 chickens left by the time all the ducks were sold. However if the ducks sold was thrice the number of chicken sold, there would be 330 chickens left by the time all the ducks were sold.
(a) total number of chickens and ducks on farm.
(b)What was the ratio of the number of ducks to the number chickens?

4. There are some apples and pears in a box. If 3 apples are remove, the number of apples will be 1/5 of the total number of fruits left. If 10 pears are removed, the number of apples will be 1/3 of the total number of fruits left. How many pears are there?

Qn1)

Total amt Jerry had at first => $176 + Remainder = $176 + 7parts = 15u
6/7 of remainder => $110 + 1u = 6parts

1u = 6 parts - $110
15u = 90 parts - $1650

90parts - $1650 = $176 + 7parts
83 parts = $1826
1part = $22
Amt Jerry had at first = $176 + 7($22) = $330

Qn2)

Swee Long : Total = 1 : 5 = 4 : 20
Rafi : Total = 1 : 4 = 5 : 20
Ted : Total = 1 : 2 = 10 : 20

Total no. of stamps = 20
Swee Long gets 4, Rafi gets 5 and Ted gets 10; and 1 stamp is left.

Qn3)

1) If no. of chicken sold is 3 times the no. of ducks sold

At first
Chicken : 90 + 3u
Ducks : 1u

2) If no. of ducks sold is 3 times the no. of chicken sold
At first
Chicken : 1p + 330
Duck : 3p

1u = 3p
90 + 3(3p) = 1p + 330
8p = 240
1p = 30
1u = 90

a)\tTotal no. of chicken and ducks = 4u + 90 = 4(90) + 90 = 450
b)\tRatio of ducks : chicken = 3(30) : 30 + 330 = 90 : 360 = 1 : 4


Qn 4)

Before the 3 apples are removed
Apples : 1u + 3
Pears : 4u

Before the 10 pears are removed
Apples : 1p
Pears : 2p + 10

1u + 3 = 1p
4u = 2p + 10
4u = 2(1u + 3) + 10
4u = 2u + 16
2u = 16
1u = 8
1p = 8 + 3 = 11
No. of pears = 4( 8 ) = 32

[SKT]

Thank you Dharma.

[Herbie]

I have one qn.


15. A bullet train took 5 hours to travel from Patient Town to Honest Town while an electric train took 4 hours longer to travel from Honest Town to Patient Town. Both trains set off at the same time and moved towards each other. Two hours later, they were 255 km apart. What was the speed of the electric train?

CHIJ St Nicholas 2009

[corneyAmber]

http://i724.photobucket.com/albums/ww246/ks2me/P6Mathmeal.jpg\">