Q&A - PSLE Math

[Swift Formula]

At 10.00 am Joash was cycling from Mivo city towards Purmei town. At the same time , Miriam was cycling from Purmei town towards Mivo city on the same route as Joash. Cycling at a speed of 4 km/h faster than MIriam, they would pass each other 400 meters away from the midpoint .
What time did they pass each other?

If Joash took another 4 minutes to reach Purmei town, what time would Miriam reach Mivo city?

I use timeline for clear presentation.

Using "Distance = Speed x Time" as the formula

Time travel to midpoint is same between Joash and Miriam
Difference in Distance travelled = midpoint + 400m - (midpoint - 400m) = 800m
Speed difference = 4 km/h as given

So in order to make a difference in distance of 800m using the speed difference of 4 km/h, Time taken = ???

Do you still need further help?

[COOKIE64]

Please help , I tried solving the simultaneous equations I am getting the answers in fractions?

[Swift Formula]

Please help , I tried solving the simultaneous equations I am getting the answers in fractions?

Gave 2 wrong equations.
Try again.

[pirate]

At 10.00 am Joash was cycling from Mivo city towards Purmei town. At the same time , Miriam was cycling from Purmei town towards Mivo city on the same route as Joash. Cycling at a speed of 4 km/h faster than MIriam, they would pass each other 400 meters away from the midpoint .
What time did they pass each other?

If Joash took another 4 minutes to reach Purmei town, what time would Miriam reach Mivo city?

I use timeline for clear presentation.

Using "Distance = Speed x Time" as the formula

Time travel to midpoint is same between Joash and Miriam
Difference in Distance travelled = midpoint + 400m - (midpoint - 400m) = 800m
Speed difference = 4 km/h as given

So in order to make a difference in distance of 800m using the speed difference of 4 km/h, Time taken = ???

Do you still need further help?

I was going to do it the traditional equation way, then I realized that I was a dum-dum.

Mivo --- x km --- | --- 0.4 km --- | --- 0.4 km --- | --- x km --- Purmei

It took Joash another 4 minutes to reach Mivo, ie Joash took 4 minutes to travel x km; and 12 minutes to travel x + 0.4km + 0.4km

Therefore Joash took 12 + 4 = 16 minutes to travel the entire distance.

It took Joash 16 - 4 - 4 = 8 minutes to travel 2x km, and also 8 minutes to travel 2*0.4km
Therefore x = 0.4km. Total distance = 4x or 1.6 km.

Since it took Miriam 12 minutes to travel x km, it will take Miriam a total of 4*12 = 48 minutes to reach Purmei from Mivo.

Therefore Miriam arrived at Purmei at 10.48am.

No need for any complicated equations.

[DearSonR]

At 10.00 am Joash was cycling from Mivo city towards Purmei town. At the same time , Miriam was cycling from Purmei town towards Mivo city on the same route as Joash. Cycling at a speed of 4 km/h faster than MIriam, they would pass each other 400 meters away from the midpoint .
What time did they pass each other?

If Joash took another 4 minutes to reach Purmei town, what time would Miriam reach Mivo city?

If Joash was 4km/h slower, both of them would have traveled an equal distance.
But since, Joash traveled 4km/h faster than Miriam, then Joash traveled an additional 0.8km.
So, to find the amount of time which passed when both of them met, just take:
0.8km/4km/h=1/5h=12min
10.00am-->12min-->10.12am

So, they passed each other at 10.12am.


Joash:Miriam
Speed 3 : 1
Time 1 : 3

The ratio of above is like that because:
It took another 4min for Joash to reach Purmei Town. So, 12/4=3. Joash traveled 3 units when Miriam only traveled 1 unit. The ratio of time is just the ratio of speed flipped over. The difference in their speeds is 4km/h. So, 3 units-1unit=2 units, 2 units is 4km/h, 1 unit is 2km/h and 3 units is 6km/h. 6km/h*12min=1.6km. 1.6km/2km/h=4/5h=48min.
10.00am-->48min-->10.48am

Miriam would reach Mivo City at 10.48am.

[GingerCub]

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Very helpful for students.

Are you mocking homework by creating that site?

no, not at all, im sure it is very important what ur doing here

[Swift Formula]

Well done pirate and DearSon. I didn't read your solution but I am pretty sure it is correct.

I only show the first part of my method. The rest is not given because it would be bad to give answer straight to the person posting question.
If parents, it's ok.
I do not encourage students to seek answer directly from this forum, because I wish students would take some time to study and explore the question, try as much as possible to solve their own question instead of copying the solution provided.
Good morning to Singapore ~

[COOKIE64]

Daniel and his friends wanted to paint the rooms of a new house. If they paint 6 rooms per day they will be able to complete painting all the rooms ahead of time by 1 day . If they paint 4 rooms per day they will be behind schedule by 2 days . How many rooms are there in the house ?

[Swift Formula]

Daniel and his friends wanted to paint the rooms of a new house. If they paint 6 rooms per day they will be able to complete painting all the rooms ahead of time by 1 day . If they paint 4 rooms per day they will be behind schedule by 2 days . How many rooms are there in the house ?

This question is usually directly proportional and inversely proportional type of question.
But this question fixed the number of workers. The only variable is Rooms Per Day (RPM) and Number of Days.

(Let the estimated original number of days be A)
6 RPM = 1 day earlier
4 RPM = 2 days later

6x (A-1) = 4x (A+2)

Do you still require further explanation?

[Nebbermind]

Daniel and his friends wanted to paint the rooms of a new house. If they paint 6 rooms per day they will be able to complete painting all the rooms ahead of time by 1 day . If they paint 4 rooms per day they will be behind schedule by 2 days . How many rooms are there in the house ?

If they paint four rooms, they are 3 days slower, ie, they still have 12 rooms to paint.

If they finish in X days for 6/day, there are 6X rooms.

Therefore, 6X = 4X + 12
X = 6

Total rooms = 6 x 6 = 36

(6 days vs 9 days)