PSLEguru:

yanling had 60% more stamps than lena.
so lena can be 10u and yanling can be 16u.
tricia had 75% fewer stamps than yanling.
so tricia = 0.25 * 16u = 4u.

yes 16u is 160% and 10u is 100%.

and yes i'm sure there are other ways to arrive at a solution. I just happened to use this method.

this seems to be a difference problem as there are statements to describe the difference. Could you show us the technique that you introduced in your article on Difference problems for this question ?

MathIzzzFun:

mathnoobs:

[quote=\"MathIzzzFun\"]

alternate approach using model/units

http://i39.tinypic.com/f5aef8.jpg\">

cheers.

I'm afraid I'm a bit lost on the how you derive the value 10 in
5u - 80 = 4u + 10

the end ratio of number of 50c : 20c = 3 : 2
number of 50c in the end -> 6u + 15 = 3 x (2u+5) (as shown in model)
so, number of 20c --> 2 x (2u+5)

cheers.[/quote]thanks MathIzzfun, I understand now.

MathIzzzFun:

alternate approach using model/units

http://i39.tinypic.com/f5aef8.jpg\">

cheers.

I'm afraid I'm a bit lost on the how you derive the value 10 in
5u - 80 = 4u + 10

MathIzzzFun:

mathnoobs:

[quote=\"MathIzzzFun\"]

A rectangular tank measuring 250cm by 40cm by 100cm was 1/4 filled with water. Tap A was then fitted and had water flowing into the tank at a rate of 5 litres per minute and tap B had water drained out from the tank at the rate of 2 litres per minute.Tap A was turned on for 3 minutes and then it was turned off. Immediately after Tap A was turned off, Tap B was turned on for 3 minutes and then it was turned off. The 2 steps were repeated until the tank was completely filled without water overflowing. How long did it take for the tank to be filled ?

This is a variation of the \"snail climbing up wall\" question ... ie the snail moves up 3 cm and then slips 2 cm over certain time.

We can either use volume/flow rate or just using the height/\"height rate\" (convert the flow rate to \"height rate\" using height rate = flow rate / base area)

using volume...

volume of tank = 250cm x 40cm x 100cm = 1000 ℓ
remaining volume to fill = 3/4 x 1000ℓ = 750ℓ

In 3 min, volume filled by tap A = 5ℓ x 3 = 15ℓ

In 6 min (1 fill cycle), volume filled by tap A and B = (5-2) x 3ℓ = 9ℓ

assuming that the last 15ℓ will be filled by tap A, 750ℓ-15ℓ = 735ℓ to be filled

number of fill cycles = 735/9 = 81 2/3 --> take 82 fill cycles
In 82 fill cycles, volume filled --> 82 x 9ℓ = 738ℓ ----- in 82 x 6 min= 492 min

Time taken for Tap A to fill remaining volume of (750ℓ-738ℓ) = 12ℓ
--> 12/15 x 3 min = 2.4 min
7
total time to fill to brim --> 492 min + 2.4 min = 494.4 min5

cheers.

Hi Mathzizzfun
I’m afraid I don quite get why the assumption is last 15 liters.
If 83 cycles is used instead of 82 cycles, that will give 83x9 = 747 liters and a remaining 3 liters to reach 750 liters.
Why not have the maximum cycles ?

The fill cycle comprise of tap A filling for 3 min n tap B draining for 3 min. Both taps are not turned on t the same time.

Instead of doing +15-6+15-6... we assume one fill cycle to fill 9l in 6 min.

Suppose we have only 9L to fill, the time taken is not 6min because it will take less than 2min for tap A to fill 9l.
so when we take 750÷9= 83r3
The final fill cycle (83th cycle ) is actually adding 15l first n then draining 6l. This means that we would need an imaginery overflow container to hold the exess water n then drain this away in the next 3 min, n then adding the final 3l. So, this is incorrect.

cheers.[/quote]Thank you MathIzzfun, I understand now.

MathIzzzFun:

A rectangular tank measuring 250cm by 40cm by 100cm was 1/4 filled with water. Tap A was then fitted and had water flowing into the tank at a rate of 5 litres per minute and tap B had water drained out from the tank at the rate of 2 litres per minute.Tap A was turned on for 3 minutes and then it was turned off. Immediately after Tap A was turned off, Tap B was turned on for 3 minutes and then it was turned off. The 2 steps were repeated until the tank was completely filled without water overflowing. How long did it take for the tank to be filled ?

This is a variation of the \"snail climbing up wall\" question ... ie the snail moves up 3 cm and then slips 2 cm over certain time.

We can either use volume/flow rate or just using the height/\"height rate\" (convert the flow rate to \"height rate\" using height rate = flow rate / base area)

using volume...

volume of tank = 250cm x 40cm x 100cm = 1000 ℓ
remaining volume to fill = 3/4 x 1000ℓ = 750ℓ

In 3 min, volume filled by tap A = 5ℓ x 3 = 15ℓ

In 6 min (1 fill cycle), volume filled by tap A and B = (5-2) x 3ℓ = 9ℓ

assuming that the last 15ℓ will be filled by tap A, 750ℓ-15ℓ = 735ℓ to be filled

number of fill cycles = 735/9 = 81 2/3 --> take 82 fill cycles
In 82 fill cycles, volume filled --> 82 x 9ℓ = 738ℓ ----- in 82 x 6 min= 492 min

Time taken for Tap A to fill remaining volume of (750ℓ-738ℓ) = 12ℓ
--> 12/15 x 3 min = 2.4 min
7
total time to fill to brim --> 492 min + 2.4 min = 494.4 min5

cheers.

Hi Mathzizzfun
I’m afraid I don quite get why the assumption is last 15 liters.
If 83 cycles is used instead of 82 cycles, that will give 83x9 = 747 liters and a remaining 3 liters to reach 750 liters.
Why not have the maximum cycles ?

MathIzzzFun:

mathnoobs:

Hi MathIzzzFun
I’m afraid I don’t quite understand how to simplify the following expression:
(18 units – 60km)/9units x 18
In your example, this will simplify to 36 units – 120 km
I’m stuck at how to eliminate the 9units from the denominator.

thanks

oops ... you are right..thanks for highlighting the error.. my apologies.
For this case, there will be no solution as the resultant quadratic equation will yield no real roots.

In order to get a real value for the speed, the question should be amended as follows:

Mr Tan travelled from Town A to Town B at 11:00. When he was 18 km from Town A , Mr Bala left Town B to Town A at a speed of 18km/h faster than Mr Tan. When Mr Bala reached Town A at 13:00, Mr Tan had completed 90 percent of his journey. What was Mr Tan's average speed?

in this case,
Mr Tan's speed --> 54 km/h and
Bala's speed --> 72 km/h

cheers.

thanks MathIzzzFun for the clarification. It is clearer now.

MathIzzzFun:

http://i40.tinypic.com/ztj18k.png\">

looks like both are cyclists and Bala is certainly a pro-racer.

cheers.

Hi MathIzzzFun
I’m afraid I don’t quite understand how to simplify the following expression:
(18 units – 60km)/9units x 18
In your example, this will simplify to 36 units – 120 km
I’m stuck at how to eliminate the 9units from the denominator.

thanks

thanks MathIzzFun and ICreativeMath, I understand now. Appreciate you spending time on the explanations.

Barley Tower:

A coin box contained only twenty-cent and fifty-cent coins in the ratio of 4:5. When 16 fifty-cent coins were taken out and replaced by some twenty-cent coins, the number of fifty-cent coins left in the box was 7/8 of the twenty-cent coins. The total value of all the coins remained the same. Find the sum of money in the coin box.


Hi nnchia, you might want to consider this method without using algebra which some children may find too abstract and may not understand.


16 50-cent coins = $ 8.00 which is 40 20-cents coins.\t\t
\t\t
Now:\t\t
Since the Ratio of 20 cents coins to 50-cents coins is 8:7\t\t

20-cents coins: \t8 Units + 40\t
50-cents coins: \t7 Units + 35 \t
\t\t
At First:\t\t
To work backward to the At-First situation, deduct 40 20-cents coins and add back 16 50-cents coints\t\t

20-cents coins: \t8 Units\t
50-cents coins: \t7 Units + 35 + 16\t
\t\t
We are also given that At First, the ratio of 20-cent coins to 50-cents coins is 4:5
\t\t
Hence, if there are 8 units of 20-cent coins, there must be 10 units of 50-cents coins.
\t\t
20-cents coins: \t8 Units\t
50-cents coins: \t10 Units\t
\t\t
Compare the 50-cents coins:

10 Units = 7 Units + 51\t\t
3 units = 51 coins\t\t
1 unit = 17 coins\t\t
\t\t
At first, there are 17 X 8 = 136 20-cents coins and 17 X 10 = 170 50-cents coins.
\t\t
Total value of the coins is $ 27.20 + $ 85.00 = $ 112.20.

I'm quite confused by this:
20-cents coins: \t8 Units + 40\t
50-cents coins: \t7 Units + 35 \t
is that the Before value or the After value ? and if so, how was it derived ? don't know where the 35 comes from.
This method not so easy to understand

MathIzzzFun:

Oldschool:

Hi,


(1) 2 teams will take 30 days to complete.

Then, 30 days => 100%

So, in 6 days, the 2 teams completed => 100/30 x 6 = 20%

(2) Therefore, left with 80% which was completed by a single team in 40 days.

80% => 40 days
100% => 50 days

(3) Assume that both teams are equally hardworking. Then it would take 50 days for a single team to complete that certain job.

Regards

the two team worked at different rate.

Total amount of work to be done --> 30 units (1 day = 1unit of work)

In 6 days, 6 units completed, 24 units left.

Team A (team remained to complete the work) takes 40 days to complete 24 units of work --> 24/40 unit/day = 0.6 unit/day

Team B --> (1 - 0.6) unit/day = 0.4unit /day

Number of days taken by each team to complete all the work by itself:
Team A --> 30/0.6 = 50 days
Team B --> 30/0.4 = 75 days

cheers.

could someone post the question to this answer ? it would be useful.