Q&A - PSLE Math

[tianzhu]

lousymum:

Help pls.

(1) Michael jogged while Karen walked from the same place but in opposite directions along a straight road. After 5h, they were 30 km apart. Michael's average speed was 1.2 km/h faster than Karen's average speed. What was Karen's average walking speed?

Hi

There’s a few ways to solve it.

For questions on Speed, it’s useful to start with a simple diagram.

If Karen’s distance travelled in 5h is showed by 1 unit or 1 box, then Michael’s distance travelled in 5h would be 1 unit or 1 box + (5*1.2)

Hence we have 2 boxes or units + 6 ------- 30

This gives 1 unit/box ------- 12

Therefore, Karen’s speed -------- 12/5 ------- 2.4

Best wishes

[tianzhu]

lousymum:

(2) Ben and Macus received some moey from their mother. Marcus would have $64 more than Ben if Ben gave 2/5 of his share to Marcus. Marcus would have $144 more than Ben if Ben gave 2/3 of his share to Marcus. How much money did Ben receive from his mother?

Hi

There are two scenarios in this question.

Marcus would have $64 more than Ben if Ben gave 2/5 of his share to Marcus.

A common multiple of 3 and 5 is 15

Marcus -------9 units + 64
Ben -------- 9 units

Marcus would have $144 more than Ben if Ben gave 2/3 of his share to Marcus

Marcus -------5 units + 144
Ben -------- 5 units

The total amount of money in both scenarios stays the same.

18 units + 64 ------- 10 units + 144
8 units -------- 80
1 unit ------- 10

Ben ------- 15 units -------- 150

Best wishes

[lousymum]

Hi tianzhu,


hmm... yr answers are so much easiler to digest, :thankyou:

[koguma]

tianzhu:

lousymum:

Help pls.

(1) Michael jogged while Karen walked from the same place but in opposite directions along a straight road. After 5h, they were 30 km apart. Michael's average speed was 1.2 km/h faster than Karen's average speed. What was Karen's average walking speed?

Hi

There’s a few ways to solve it.

For questions on Speed, it’s useful to start with a simple diagram.

If Karen’s distance travelled in 5h is showed by 1 unit or 1 box, then Michael’s distance travelled in 5h would be 1 unit or 1 box + (5*1.2)

Hence we have 2 boxes or units + 6 ------- 30

This gives 1 unit/box ------- 12

Therefore, Karen’s speed -------- 12/5 ------- 2.4

Best wishes

Hi Tianzhu, I tried to following your steps for the following qns but I get stuck. Appreciate if you can advise on this qns. Thanks.

A cargo train leaves city X for city Y, 1500km apart at 8am. At the same time, express train leaves city Y for city X. Express train travels at a speed 100km/h faster than cargo train.
The 2 trains pass each other and they are 300km apart at 8pm. What is the speed of express train?

[tianzhu]

Hi koguma


Please refer to MathIzzzFun’s solution.

Best wishes

[MathIzzzFun]

koguma:

A cargo train leaves city X for city Y, 1500km apart at 8am. At the same time, express train leaves city Y for city X. Express train travels at a speed 100km/h faster than cargo train.
The 2 trains pass each other and they are 300km apart at 8pm. What is the speed of express train?

Hi

Draw a diagram for the journey..
1st part of the journey -- cargo train and express train meet --> total distance travelled (by both) = 1500 km
2nd part of journey -- cargo train and express train \"separate\" and go opposite way --> additional distance covered = 300 km in total.
Total distance covered in 1st part & 2nd part of journey --> 1800 km --(A)

Since express train travels 100 km/h faster, after 12 hours (8am to 8pm), the express train will cover 100 km x 12 h = 1200 km more than the cargo train.

So, distance covered by express train --> (1800 + 1200) / 2 = 1500 km
Express train's speed --> 125 km/h
Cargo train's speed --> 25 km/h

or ..from (A) and total time from 8am - 8pm = 12h,
total speed (cargo + express) = 1800 km/ 12h = 150 km/h
since express train's speed is 100 km/h more than cargo train,
express train's speed --> (150 + 100) /2 = 125 km/h

cheers.

[Chan09]

Why would you divide by 2?

distance covered by express train –> (1800 + 1200) / 2 = 1500 km

[MathIzzzFun]

Chan09:

Why would you divide by 2?

distance covered by express train --> (1800 + 1200) / 2 = 1500 km

Hi

Draw a simple model,
Bigger block--> expres train
Smaller block --> cargo train
Sum = 1800
Difference = 1200

cheers.

[Neat]

Hi


Tap A can fill a tank completely in 6 minutes. Tap B can fill the same tank completely in 3 minutes. At the beginning, Tap A was turned on to fill the tank. After 1 minute, Tap B was then turned on to fill the tank. How long would it take to fill the tank completely?

Thanks for the time.

[Edureach]

Neat:

Hi


Tap A can fill a tank completely in 6 minutes. Tap B can fill the same tank completely in 3 minutes. At the beginning, Tap A was turned on to fill the tank. After 1 minute, Tap B was then turned on to fill the tank. How long would it take to fill the tank completely?

Thanks for the time.

Let the volume of the tank be in 6 units.

Speed of tap A to fill 1 unit = 1min/6mins for 6 units.
Speed of tap B to fill 1 unit = 30 secs/3mins for 6 units.

Tap A was turned on during 1st min = 1 unit filled.
Tap A & B were turned on during next min = 1+2 units filled.
Time taken to filled 4 units = 2 mins Ans(A).
Balance 2 units to be filled by tap A and B.

It took 60 secs to fill 3 units.
For 2 units time taken = 60 x 2/3 = 40 secs Ans (B).

Total time taken to fill completely = Ans A +B = 2 mins 40 secs.