## Wednesday, June 8, 2011

### June Vacation Chap 9.2 RATE (L5) Can he catch up with her?

Grace left home at 6.30 am to walk to school. 10 minutes later, her brother Shamus saw her wallet on the dining table. He grabbed the wallet and hopped onto his bicycle and rode after Grace.

Shamus rode his bicycle 3 times as fast as Grace walked.
Q1: What time was it when Shamus caught up with Grace?
Q2: If the school is 800m from home, did Shamus reach Grace before she arrived at school?

Use the following to guide you...
• What information do you know from the problem?
• What else do you need to know to solve the problem?
• Pick a reasonable number for the information you need.

1. 1) 6.45 am

2)assuming the speed Grace walk at was 20m/min, then no.(I assume because the speed of Grace is not stated and therefore, the question is insolvable unless i take a assumption)

2. 1) The time would be 6.45am when Shamus had caught up with Grace.

2) Shamus did not reach Grace.Assume Grace speed is 5m/s and Shamus speed is 15m/s. They will take 15 min to reach. 15min=900 seconds. Thus take 5(x)900=4500m. 4500m is greater than 800m. Thus, Shamus would not be able to catch up with her.

3. 1) 6.45am

2) This question requires either the speed of Shamus or Grace in order to be solved. With the current available facts, almost any answer is possible. Let me explain:

(i)
Assuming that they meet at 6.45am at the school, Grace's speed = 800/15 = 53.333 m/min, and Shamus' speed = 53.333 x 3 = 160 m/min.

(ii)
However, we do not know for sure the speed of either Grace or Shamus to find out the distance travelled by each of them at 6.45 am.

(iii)
To demonstrate this point further, assume that Grace's speed is 40m/min. Shamus speed = 40 x 3 = 120 m/min. At 6:45 am, Grace travelled 40 x 15 = 600m while Shamus travelled 120 x 5 = 600 m as well. This would mean that they met BEFORE Grace arrived at the school. This situation differs starkly from the situation in (i).

This proves that with different speeds of Grace (and Shamus), different conclusions will be reached.

4. Hoong Teng Jun Wilbur6/12/2011 09:44:00 PM

1)6.45am

2)the question is not solvable as the speed is not stated

what information do i know from the problem:
we know the distance from home to school
shamus speed is three times of grace
he only noticed the wallet 10minutes later
grace left home at 6.30am

what else do i need to know to solve the problem
we need to know the speed of grace

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7. 1)6.45a.m
2)It depends on the speed of Grace.If Grace speed is higher than 53.333333....m/min ,It will be possible for Shamus to reach grace before she reaches school.If not it is not possible for him to reach grace before she reaches her school.

8. 1)6.45 a.m.
2)It is impossible to tell as the speed is not given and the only given data are the distance between the home and the school,shamus is three times faster then his sister and that shamus left the house at 6.40 while grace left at 6.30.We need 1 of the following person's speed to solve the question.

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10. 1. 6.45 a.m.
2. The information needed to find out the answer to this question is the rate of how much distance on of them can cover in a period of time. But it is not given so it cant be answered.

11. 1. 6.45 a.m.

2.Shamus would not reach grace before she reached the school as if we assume the speed of grace is 10m/s and shamas is 30m/s.
Grace would take 80s that is not possible... and shamas would take 25.6667 seconds but as he is 10 minute late he would not be able to catch up with her.

12. 1) 6.45 a.m.

2) We do not have the speed of Shamus or his sister, thus it is impossible to find the distance travelled, being unable to solve this question.

13. 1) 6.45a.m.
2)Assuming the speed of Grace is 10 metres /minute, making Shamus moving at the speed of 30 metres/minute. So Within 10minutes, Grace would have moved 100metres. From there, her brother started to move. So that means that Shamus will travel 300 metres in 10 minutes which is over Grace's speed, so he wouls be able to catch up with Grace within 10 minutes.

14. 1) 6.45am
2) To be able to find out the answer for this question the speed of Grace or Shamus is needed.

Assuming that the speed of Grace is 50m/min, Shamus' speed would be 150m/min. 10 minutes later Grace would already be 500m away from home while Shamus would still be at home. As Shamus is riding on a bicycle, the difference in speed between Shamus and Grace would be 100m/min which means that every 50m Grace moves Shamus would be 100m closer to her. To find the time taken to travel to her we would have to take the distance Grace has already walked divided by the difference in speed, which would give us 5 minutes. In 5 minutes Grace would have walked an additional 250m which will total up to (500m + 250m) 750m so Shamus would be able to reach Grace before she arrived at school.

15. The time would be 6.45am

The question is not solvable.

16. Q1:6.45am

Q2:Question needs the speed of Grace/Shamus before being able to be solved

17. 1. 6.45 am

2. We will need either the speed of Shamus or Grace to work out the solution.

18. 1. 6.45am

2. I have know the speed of Shamus or Grace to find out whether Shamus reached Grace before she reached school as the answer could be anything because the difference in speed is 3 times.

19. 1) 6.45am

2) Shamus was able to reach Grace before she arrived at school. Knowing that Shamus is travelling 3 times faster than Grace, he is able to catch up with her. Assuming that Grace is travelling at a speed of 10m/min. She will take 80 minutes to walk from home to school. If Shamus is travelling 3 times faster than Grace, his speed will be 30m/min. At this rate, Shamus will be able to arrive at school in 26.67 minutes. Therefore, Shamus will be able to reach Grace before she arrives at school.

20. 1)6.45am

2) Detailed information is needed to solve the problem so therefore it is not solvable.

21. 1) 6.45am

2)Shamus was able to reach Grace before she got to school. Assuming that Grace's speed was 20m/min, Shamus' speed would be 60m/min.Grace had already walked 200m (20m x 10min) when Shamus left the house. Grace would reach school at 7.20am at the pace she is travelling at, taking a total of 40 minutes. (800m/20m/min, 6.40 + 40min) Shamus would reach her school in 13.37min. So Shamus would be able to catch up with Grace.