Q&A - PSLE Math

[tianzhu]

Hifive:

Hi tianzhu


Thanks for your explanation, now I can understand the steps better.

Have a nice day!

Hi Hifive

You're welcome.

Best wishes

[Leanne]

Can someone pls help me with this speed question?thanks alot.


N and X jogged to and fro repeatedly along a straight path in a park between two points A and B.N jogged at a uniform speed of 4/s and Z jogged at a uniform speed of 6m/s.They started jogging from opposite directions at the same time as show below.

\t\t\t\t\t N towards> \t <towards Z
A______________________________________________________________B
\t x Y\t\t
They first met one another at point X.The second time they met was at point Y.
a)\tGiven that the distance between X and Y is 160m.Find the distance between A and B.
b)\tIf they started jogging at 8am,how long did they take to meet again for the third time?(Express your answers in mins and seconds)


Regards,
Leanne

[tianzhu]

Leanne:

N and X jogged to and fro repeatedly along a straight path in a park between two points A and B.N jogged at a uniform speed of 4/s and Z jogged at a uniform speed of 6m/s.They started jogging from opposite directions at the same time as show below.

\t\t\t\t\t N towards> \t <towards Z
A______________________________________________________________B
\t x Y\t\t
They first met one another at point X.The second time they met was at point Y.
a)Given that the distance between X and Y is 160m.Find the distance between A and B.
b)If they started jogging at 8am,how long did they take to meet again for the third time?(Express your answers in mins and seconds)

Hi

I think there is a typo error here, should be read as N and Z.

To begin with, may I suggest you start with a simple distance/time line.

Let’s look at this question from this perspective.

In any given duration of time, if you drive twice as fast, you’ll go twice as far.

Hence, Z covered more distance than N in a given time.

In 1 second, Z covered 6m and N covered 4m

Draw a distance line, you may say Z covered 3 units and N covered 2 units. (6:4)

5 units ------Distance between A and B

From the distance line, you’ll observe that the distance between X and Y is 2 units.

Given 2 units ----- 160m

Therefore, 5 units -----400m, this is the distance between A and B.

For N and Z to meet a third time, N must run from A to B and then back to A again.Observe the movement along the distance line.

400*2 ----800
800/4 ----200s -----3 min 20 secs

Best wishes

[Dharma]

When N and Z are at each end (i.e. at points A and B respectively), they have to jog towards each other for them to meet.


So, the total distance jogged by N and Z before they meet each other for the 1st time at Point X is the distance from A to B.

Since they started at the same time, they would have taken the same time (duration) before they meet. Therefore the distance covered by N and Z will be proportional to their speeds.

Speed ratio => N : Z = 2 : 3
Distance ratio => N : Z = 2 : 3

N will have to jog a distance of 2 units from Point A to Point X while Z will to jog a distance of 3 units from Point B to Point X

After the 1st meeting, N and Z will jog in opposite directions until they reach Points B and A respectively, and then they turn back and jog again towards each other unitl they meet at Point Y.

From the 1st meeting point to the 2nd meeting point, N and Z will have travelled a total of 2 times the distance of Point A to B. This means that N will have to travel 4 units and Z will have to travel another 6 units from Point X to Y

Distance travelled by Z = 2 units + 2 units + 160m = 2 x 3 units
6 units = 4 units + 160m
1 unit = 80m
Total distance from A to B = 5 units = 5 x 80m = 400m

Total distance that Z jogged before meeting N for the 3rd time
= 3 units + 6 units + 6 units
= 15 units
= 15 x 80m
= 1200m

Time taken by Z = 1200m/(6m/s) = 200s = 3mins 20s

[Leanne]

Hi Tianzhu and Dharma,

Thanks for the reply and explanation.

Have another one, could u pls help as am trying to think through it.thanks again.

12 At 9 am,Gopal left village A and drove towards the city at an average speed of 60km/h.Two hours later, Ali also left village A and drove along the same route as Gopal.After traveling 270km,Ali managed to catch up with Gopal.
(a)\tWhat was the average speed at which Ali traveled?
(b)\tHow far apart would they be at 3p.m.?

[Dharma]

Leanne:

Hi Tianzhu and Dharma,

Thanks for the reply and explanation.

Have another one, could u pls help as am trying to think through it.thanks again.

12 At 9 am,Gopal left village A and drove towards the city at an average speed of 60km/h.Two hours later, Ali also left village A and drove along the same route as Gopal.After traveling 270km,Ali managed to catch up with Gopal.
(a)\tWhat was the average speed at which Ali traveled?
(b)\tHow far apart would they be at 3p.m.?

In 2 hours, Gopal would have travelled 120km (60km/h x 2 hrs)
Gopal travels another 150km (270km – 120km) before Ali catches up with him

Gopal travels 150km in the same time that Ali travels 270km
Distance ratio of Gopal : Ali = 15 : 27 = 5 : 9
Speed ratio of Gopal : Ali = 5 : 9

5 units = 60km/h
9 units = 108km/h

Time taken for Ali to catch up with Gopal = 270km/(108km/h) = 2.5 hours
Ali catches up with Gopal at 12.30pm

Difference in distance travelled at 3pm = (108 – 60)km/h x 3.5hrs = 168km

[tianzhu]

Dharma:

Time taken for Ali to catch up with Gopal = 270km/(108km/h) = 2.5 hours
Ali catches up with Gopal at 12.30pm

Hi Dharma

Good Afternoon

Ali travelled for 2.5 hours.He started at 11am.

He should catch up with Gopal at 1.30pm.

Best wishes

[Dharma]

tianzhu:

Dharma:

Time taken for Ali to catch up with Gopal = 270km/(108km/h) = 2.5 hours
Ali catches up with Gopal at 12.30pm

Hi Dharma

Good Afternoon

Ali travelled for 2.5 hours.He started at 11am.

He should catch up with Gopal at 1.30pm.

Best wishes

Thanks Tianzhu. Amended solution.

In 2 hours, Gopal would have travelled 120km (60km/h x 2 hrs)
Gopal travels another 150km (270km – 120km) before Ali catches up with him

Gopal travels 150km in the same time that Ali travels 270km
Distance ratio of Gopal : Ali = 15 : 27 = 5 : 9
Speed ratio of Gopal : Ali = 5 : 9

5 units = 60km/h
9 units = 108km/h

Time taken for Ali to catch up with Gopal = 270km/(108km/h) = 2.5 hours
Ali catches up with Gopal at 1.30pm
Difference in distance travelled at 3pm = (108 – 60)km/h x 1.5hrs = 72km

[mum2010]

Please help!


Benny has 24 notes which totals to $168. They are in two-dollar, five-doller adn ten-dollar denominations. How many of each kind of notes does he have?

On tree-planning day, 40 people planted some trees. Each man planted 3 trees and each woman planted 2 trees. The men planted 35 more trees than the woman. How many men and women were there?

Mary put some fifty-dollar notes and some ten-dollar notes into a piggy bank. There were a total of 60 notes. The total value of the fifyt-dollar notes and ten-dollar notes was equal. How much money did she put into the piggy bank?

TIA.

[tianzhu]

mum2010:

Benny has 24 notes which totals to $168. They are in two-dollar, five-doller adn ten-dollar denominations. How many of each kind of notes does he have?

Hi

Is there any missing information in this question?For example, the relationship in the number of notes.

Best wishes