### 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. Q1. 6.45am
Q2. Speed is not indicated, so it is not possible to find out.

2. Q1.
Grace - 6.30am
Shamus - 6.40am
Grace - x m/min
Shamus - 3x m/min
In ten minutes, Grace - 10x
6.41am - Grace 11x Shamus - 3x
6.42am - Grace 12x Shamus - 6x
6.43am - Grace 13x Shamus - 9x
6.44am - Grace 14x Shamus - 12x
6.45am - Grace 15x Shamus - 15x Ans: 6.45am
Alternative Method:
Multiples of 3 : 3,6,9,12,15,18
Ten Minutes: Grace - 10x
11,12,13,14,15 -they met at 15x (dist.)
15x = 15mins(Grace) 6.30am + 15mins = 6.45am Ans: 6.45am

Q2. The speed is not provided so we cannot find out the answer to this question.

3. 1. y-a part of the total distance
When Grace travelled 11y, Shamus would have travelled 3y. Time would be 6.41am.
At 6.43am, Grace would have travelled 13y, while Shamus would have travelled 9y.
This pattern shows that the gap between them is closing up.
At 6.45am, Grace would have travelled 15y and Shamus would have caught up with her after travelling 15y too.

2. As time was given only, no information on distance or speed was provided so, it is not possible to find out the answer to this question.

4. Q1. Let X be part of the total distance
Grace at 11X, Shamus 3X. 6.41a.m.
Grace at 12X, Shamus 6X. 6.42a.m.
Grace at 13X, Shamus 9X. 6.43a.m.
Grace at 14X, Shamus 12X. 6.44a.m.
Grace at 15X, Shamus 15X. 6.45a.m.

Q2. Speed has not been provided, thus we will not be able to find the answer.

5. Q1: 6.45am
Q2: Speed is not given in the question, thus it is not possible to find the answer.

6. Q1: What time was it when Shamus caught up with Grace?
6.45am
Q2: If the school is 800m from home, did Shamus reach Grace before she arrived at school?
The speed is needed to find out the answer but speed is not given.

7. 1. 6.45
2. Grace's speed is not given as t i required to solve the problem.

8. 1. 6.45am
2.speed is not mentioned so it is not possible.

9. Q1.Let x be a part of the total distance.
6.31: Grace:1x Shamus:-
6.41: Grace:11x Shamus:3x
6.42: Grace:12x Shamus:6x
6.43: Grace:13x Shamus:9x
6.44: Grace:14x Shamus:12x
6.45: Grace:15x Shamus:15x
Shamus caught up with Grace at 6.45am.

Q2. With only the given information, it is not possible to find as Grace's speed is not given.

10. Q1: At 6:45am
Q2: The speed was not given in the question therefore we cannot find the answer

11. 1)Shamus caught up with grace at 6.45am

2)Grace's speed was not mentioned so we cannot get the answer.

12. Q1) 6:45am
Q2) No speed given thus impossible to get answer

13. Q1) 6:45am
Q2) There is no information for Grace's Speed, so we cannot find the answer.

14. Q1) 10 minutes after 6.30am is 6.40am
Grace travelling at x per minute, Shamus 3x a minute.
Since Grace have already traveled 10x by 6.40am~
6.41am -> Grace: 11x; Shamus: 3x
6.42am -> Grace: 12x; Shamus: 6x
6.43am -> Grace: 13x; Shamus: 9x
6.44am -> Grace: 14x; Shamus: 12x
6.45am -> Grace: 15x; Shamus: 15x
It was 6.45am when Shamus caught up with Grace.

Q2) The speed of Grace was not included in the question, thus we cannot solve Q2

15. Q1: At 6:45am
Q2: The speed was not given

16. Question 1:
Let the distance Grace travelled in 1 min is x
Shamus travels 3x in 1 min.
6.30 a.m to 6.40 a.m is 10 mins, in which Grace would have already travelled 10x.
6.41 a.m - Grace: 11x // Shamus: 3x
6.42 a.m - Grace: 12x // Shamus: 6x
6.43 a.m - Grace: 13x // Shamus: 9x
6.44 a.m - Grace: 14x // Shamus: 12x
6.45 a.m - Grace: 15x // Shamus: 15x

Question 2: It would not be possible as speed is not given for neither Grace nor Shamus.

17. Q1) 6:45am
Q2) There is no information for Grace's Speed,so the answer is unknown

18. 1) 6.45 a.m.
2) It is not possible as their respective speeds are not given.

19. Q1)Let x a unit of distance covered every 10 mins.
At 6.30: Grace: 0 Shamus: 0
At 6.40: Grace: x Shamus: 0
At 6.50: Grace: 2x Shamus: 3x
(If Shamus continued to cycle until 6.50, he would have passed Grace. Thus, it must have been earlier than 6.50)
At 6.45: Grace: 1.5x Shamus: 1.5x (Since their distance covered is the same, this must be the time that Shamus caught up with Grace)

Q2)The speed is not given, so we can't find the answer.

20. Q1) 6.40: G=10 S=0
6.41: G=11 S=3
6.42 G=12 S=6
6.43: G=13 S=9
6.44: G=14 S=12
6.45: G-15 S=15

Ans: 6.45 am

2)It is not possible to answer as the speed is not given.

21. Some of you had made good attempts to explain your thinking in a very systematic manner. Well done!

While almost all working and answers point towards 6.45 am as the answer, there is a piece of information (available in the question) that none of you 'discovered' is a critical factor that determines the possible answer.

Has anyone got the idea what's that piece of un-used info and why it's important?

22. 1. 6.45am
2. It is impossible to do this question as it did not specify the rate of speed grace was walking at.