Q&A - PSLE Math

[MathIzzzFun]

its888me:

Nan Hua prelim 2011, Q15.


A car left Town A at 0800 and travelled to Town B at an average speed of 60 km/h. At the same time, a lorry left Town B for Town A. At 1130, the car and the lorry were 85km apart after passing each other eralier. If the car arrived at Town B at 1300, at what time would the lorry arrive at Town A?

Answer is 1400, but seems that it's not right.

TIA!

Hi

1400 is correct.

at 1130,
Distance of car from Town B --> 1.5h x 60 km/h = 90km

In 3.5h (0800-1130),
distance travelled by lorry --> 90km + 85km = 175 km
Lorry's speed = 175 /3.5 km/h = 50 km/h

Total time taken for Car to travel from Town A to Town B = 5h (from 0800 to 1300)

Total time taken for lorry from B to A = 60/50 x 5 = 6 hours
0800 + 6 hours --> 1400

cheers.

[tianzhu]

jonaandr:

1. Richard drove Cindy from Village X to Village Y at a constant speed of 60km/h.
From Village Y, Cindy walked 7km to Village Z at a speed of 4km/h.
From Village Y, Richard turned back to Village X to pick James up.
He drove along the same route at a constant speed of 60km/h to meet Cindy
at Village Z.
They reached Village Z at the same time.
Find the distance beween Village X and Village Z.

Hi

Good Morning.

Hope this helps.

Best wishes

http://farm9.staticflickr.com/8175/7940320502_ae9a78d141_z.jpg\">

[tianzhu]

jonaandr:

2. There were 124 adults in a hall. When 5/8 of the men and 4/7 of the women left the hall, the total number of men and women who remained became 48. How many men were there in the hall at first?

Hi

This question touches on simultaneous concept.

You may solve it in a pictorial manner using MD, or represent the variables with units and parts or letters of the alphabet.

Men

Left ------ 5M

Remained -------- 3M

Women

Left ------- 4W

Remained -------- 3W

3M + 3W -------- 48

1M + 1W ------- 16

5M + 4W ------- 76 (124 - 48)

4M + 4W ------ 16*4 ------ 64

1M ------ 76 – 64 ------12

Number of men@first ------ 8*12 -------- 96

Best wishes

[zanen]

Hi thanks for the previous ans. can help me with these two. thx in advance A rabbit and a tortoise competed in a 5.2 km race. The rabbit ran at a speed of 20 km/h while the tortoise’s speed was 3 km/h. The tortoise ran continuously to complete the race. However the rabbit ran for 1 min and rested for 20 min. It ran the next 2 min and rested or 20 min. It then ran for the next 3 min and rested for 20 min and so forth. At this rate, how many minutes more would it take the rabbit than the tortoise to complete the race?


Mrs Reuten bought some pizzas for a group of children. The girls received thrice as many pizzas as the boys. There were an equal number of girls and boys. Each boy ate 2/9 of a pizza and the boys finished all the pizzas given to them. Each girl ate 1/6 of a pizza and the girls had 4½ pizzas left. How many pizzas did Mrs Reuten buy?

[charsen]

zanen:

Hi thanks for the previous ans. can help me with these two. thx in advance A rabbit and a tortoise competed in a 5.2 km race. The rabbit ran at a speed of 20 km/h while the tortoise’s speed was 3 km/h. The tortoise ran continuously to complete the race. However the rabbit ran for 1 min and rested for 20 min. It ran the next 2 min and rested or 20 min. It then ran for the next 3 min and rested for 20 min and so forth. At this rate, how many minutes more would it take the rabbit than the tortoise to complete the race?


Mrs Reuten bought some pizzas for a group of children. The girls received thrice as many pizzas as the boys. There were an equal number of girls and boys. Each boy ate 2/9 of a pizza and the boys finished all the pizzas given to them. Each girl ate 1/6 of a pizza and the girls had 4½ pizzas left. How many pizzas did Mrs Reuten buy?

Hi
Q2.no. of pizzas received-->G:B
12:4
pizzas eaten----------> 1/6:2/9
3:4
pizzas left by boys to girls--->0:4.5-->0:9
9u--->4.5 pizzas
1u--->0.5 pizzas
16u---->8 pizzas(ANS)

[Zhu99]

zanen:

Hi thanks for the previous ans. can help me with these two. thx in advance A rabbit and a tortoise competed in a 5.2 km race. The rabbit ran at a speed of 20 km/h while the tortoise’s speed was 3 km/h. The tortoise ran continuously to complete the race. However the rabbit ran for 1 min and rested for 20 min. It ran the next 2 min and rested or 20 min. It then ran for the next 3 min and rested for 20 min and so forth. At this rate, how many minutes more would it take the rabbit than the tortoise to complete the race?

T : 5.2/3 x 60 = 104 min

R : 5.2/20 x 60 = 15.6 min --- run time

1 + 2 + 3 + 4 + 5 + 0.6 ---> 5 rest time
5 x 20 = 100

100 + 15.6 = 115.6 min --- total time of R

115.6 - 104 = 11.6

The rabbit took 11.6 min more than the tortoise to complete the race.

[zanen]

charsen:

zanen:

Hi thanks for the previous ans. can help me with these two. thx in advance A rabbit and a tortoise competed in a 5.2 km race. The rabbit ran at a speed of 20 km/h while the tortoise’s speed was 3 km/h. The tortoise ran continuously to complete the race. However the rabbit ran for 1 min and rested for 20 min. It ran the next 2 min and rested or 20 min. It then ran for the next 3 min and rested for 20 min and so forth. At this rate, how many minutes more would it take the rabbit than the tortoise to complete the race?


Mrs Reuten bought some pizzas for a group of children. The girls received thrice as many pizzas as the boys. There were an equal number of girls and boys. Each boy ate 2/9 of a pizza and the boys finished all the pizzas given to them. Each girl ate 1/6 of a pizza and the girls had 4½ pizzas left. How many pizzas did Mrs Reuten buy?

Hi
Q2.no. of pizzas received-->G:B
12:4
pizzas eaten----------> 1/6:2/9
3:4
pizzas left by boys to girls--->0:4.5-->0:9
9u--->4.5 pizzas
1u--->0.5 pizzas
16u---->8 pizzas(ANS)

May I know how you get 9u?

[zanen]

Zhu99:

zanen:

Hi thanks for the previous ans. can help me with these two. thx in advance A rabbit and a tortoise competed in a 5.2 km race. The rabbit ran at a speed of 20 km/h while the tortoise’s speed was 3 km/h. The tortoise ran continuously to complete the race. However the rabbit ran for 1 min and rested for 20 min. It ran the next 2 min and rested or 20 min. It then ran for the next 3 min and rested for 20 min and so forth. At this rate, how many minutes more would it take the rabbit than the tortoise to complete the race?

T : 5.2/3 x 60 = 104 min

R : 5.2/20 x 60 = 15.6 min --- run time

1 + 2 + 3 + 4 + 5 + 0.6 ---> 5 rest time
5 x 20 = 100

100 + 15.6 = 115.6 min --- total time of R

115.6 - 104 = 11.6

The rabbit took 11.6 min more than the tortoise to complete the race.

May I know why 5 rest time and not more? :scratchhead:

[tianzhu]

jonaandr:

3. Katy had a number of 20-cent coins and Jeremy had a number of 50-cent coins. Katy had 18 more coins than Jeremy but Jeremy had $8.10 more than Katy. express, to the nearest percent, the amount of money Katy had as a percentage of the amount of money Jeremy had.

Hi

Please study this solution for a similar type of question. It should help to answer your question.

I did a quick check for your question and there are 57 number of 20-cent coins and 39 number of 50-cent coins. I’ll leave you to work out the rest of the details.

Best wishes

http://farm6.staticflickr.com/5014/5557734869_1bdc3c4e23_z.jpg\">

[tianzhu]

jonaandr:

4.alicia and Bruce are given some money each. If Alicia spends three times as much as Bruce,She will have $1000 more when Bruce has spent all his money. If alicia spends half of what Bruce spends, she will have $2200 when Bruce has spent all his money. What is the total sum of money given to Alicia and Bruce?

Hi

Please study this solution for a similar type of question. It should help to answer your question.

For your question, the answers are $2440 for Alicia and $480 for Bruce. I’ll leave the rest of the details to you.

Best wishes

http://farm6.staticflickr.com/5142/5614468685_555807d62e_z.jpg\">