Q&A - PSLE Math

[Vanilla Cake]

A car and a coach travelled from Town A to Town B. The coach left Town A at 0648 and it took 5 hours to reach Town B. The car started 30 minutes later than the coach and it took 4 hours to reach Town B. At what time did the car catch up with the coach?


Information from question
(1) Both car and coach travelled the same distance from Town A to Town B meaning that distance in this case was constant.
(2) The car started 1/2 hour later and took less time than the coach to reach Town B meaning that the car travelled faster than the coach.
(3) Duration of journey for the car was 4 hours and for the coach was 5 hours.

Solution
Find the 1st common multiple of 4 and 5 and you will get 20.
This was the distance between both Towns A and B which was 20 units.

Coach took 5 hours to travel 20 units
Coach took 1 hour to travel 4 units

Car took 4 hours to travel 20 units
Car took 1 hour to travel 5 units

But the coach started 1/2 hour earlier and had travelled:
(1/2 x 4) units = 2 units.
So, the car had to catch up for this \"2 units\" of the distance.

From above, car could travel faster than the coach :
Difference in 1 hour = (5-4)units = 1 unit.
This means that for 1 hour, the car could catch up by 1 unit.
For 2 units, the car would require 2 hours.

0648.......30 min..0718..........2 hours .........0918

Hence, the car caught up with the coach at 0918 h

[Tang]

Vanilla Cake:

A car and a coach travelled from Town A to Town B. The coach left Town A at 0648 and it took 5 hours to reach Town B. The car started 30 minutes later than the coach and it took 4 hours to reach Town B. At what time did the car catch up with the coach?


Information from question
(1) Both car and coach travelled the same distance from Town A to Town B meaning that distance in this case was constant.
(2) The car started 1/2 hour later and took less time than the coach to reach Town B meaning that the car travelled faster than the coach.
(3) Duration of journey for the car was 4 hours and for the coach was 5 hours.

Solution
Find the 1st common multiple of 4 and 5 and you will get 20.
This was the distance between both Towns A and B which was 20 units.

Coach took 5 hours to travel 20 units
Coach took 1 hour to travel 4 units

Car took 4 hours to travel 20 units
Car took 1 hour to travel 5 units

But the coach started 1/2 hour earlier and had travelled:
(1/2 x 4) units = 2 units.
So, the car had to catch up for this \"2 units\" of the distance.

From above, car could travel faster than the coach :
Difference in 1 hour = (5-4)units = 1 unit.
This means that for 1 hour, the car could catch up by 1 unit.
For 2 units, the car would require 2 hours.

0648.......30 min..0718..........2 hours .........0918

Hence, the car caught up with the coach at 0918 h

5 - 4 = 1 h

1 - 1/2 = 1/2 h -> so car reached Town B 1/2 h earlier.

Hence car caught up at the mid-point, i.e after 4/2 = 2 h.

0648....30 min.......0718..........2 h .........0918

The car caught up with the coach at 0918.

[Muffins]

Hi alamak, let me (try to) solve your question:


Dist = SAME

Every 1 hour, the coach travelled 1/5 of the distance, so in 1/2 an hour, the coach would travel 1/10 of the distance. When the coach had 9/10 of the distance left, the car started from Town A. In every 1 hour, the car would travel 1/4 of the distance. So in 4 hours, the coach would have travelled 4/5 more, and 1/10 + 4/5 is 9/10. o the car reached when it had 1/10 of its distance left, which it would be able to travel in 1/2 an hour, so the car's total time, 4 hours, minus the 1/2 hour, equals 7/2 hours or 3 and a half hours. So, with a timeline, 6.48 + 3 1/2 hours equals 9.18 am, or in 24 hour time 0918.

Hope my working and answer is right!

[Dharma]

Many ways to solve the same problem. Use the method u r comfortable with. Cheers


http://www.postimage.org/

[small]

tianzhu:

Hi Dharma


Thanks for the correction.I made a mistake.(use 20% more instead of 120% more)
Price of venision per kg should be $6.55.
Price of beef per kg is $7.20.
Best wishes.

Hi small
Please consider my earlier post as null and void.
The answer is $47.80.
Best wishes

Once again, many many thanks..my DD and I misunderstood the question.

[quote]The cost of 2kg of beef is 120% more than the cost of 1kg of venison. 1kg of mutton costs 20% more than the cost of 1kg of beef.

1 kg of beef ( 160%) vs 1kg of vensison (100%)

120%/2 +100% =160% :([/quote]
:oops:

[alamak]

Hi all, thanks for all your solutions!


I see the picture now..Haha

[tianzhu]

Thank you for your help.


How to show that the sum of all angles is equal to 360 degrees?
Q35 RGPS SA2 2007

http://www.wendykoh.com/07/primary6-rgs-maths.pdf

[Tang]

tianzhu:

Thank you for your help.


How to show that the sum of all angles is equal to 360 degrees?
Q35 RGPS SA2 2007

http://www.wendykoh.com/07/primary6-rgs-maths.pdf

Partial c + d + f = 180 degree (triangle)

The other portion of c + b + a + e = 180 degree (triangle, External angle of a triangle = 2 internal opposite angles = a + e)

So all angles add up to 360 degree.

[Tang]

small:

tianzhu:

Hi Dharma


Thanks for the correction.I made a mistake.(use 20% more instead of 120% more)
Price of venision per kg should be $6.55.
Price of beef per kg is $7.20.
Best wishes.

Hi small
Please consider my earlier post as null and void.
The answer is $47.80.
Best wishes

Once again, many many thanks..my DD and I misunderstood the question.

[quote]The cost of 2kg of beef is 120% more than the cost of 1kg of venison. 1kg of mutton costs 20% more than the cost of 1kg of beef.

1 kg of beef ( 160%) vs 1kg of vensison (100%)

120%/2 +100% =160%

:oops:[/quote]
1 kg venison -> 100%

2 kg beef -> 100% + 120% = 220%
1 kg beef -> 220% /2 = 110%

[Muffins]

Tang:

tianzhu:

Thank you for your help.


How to show that the sum of all angles is equal to 360 degrees?
Q35 RGPS SA2 2007

http://www.wendykoh.com/07/primary6-rgs-maths.pdf

Partial c + d + f = 180 degree (triangle)

The other portion of c + b + a + e = 180 degree (triangle, External angle of a triangle = 2 internal opposite angles = a + e)

So all angles add up to 360 degree.

http://www.postimage.org/