## 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.

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3. I know that Grace left home at 6.30 am and Shamus left home at 6.40 am. I also know that Shamus was traveling 3 times faster than Grace.
I need to know the speed of Grace. A possible number could be 1 m/s.
Now I know that Shamus's speed is 3 m/s
When Shamus left home, Grace was 1 m/s x 600 = 600m away from home, so Shamus needed to catch up 600 m.
So, time needed for Shamus to catch up with Grace is, 600/2 = 300s = 5 mins.
Q1: Shamus caught up with Grace at 6.45 am
Total distance traveled by shamus is 300 x 3 = 900m
900 m > 800 m
Q2: Shamus will not be able to catch up with Grace

4. I know that Grace left the house at 6.30am and Shamus left the house 10 minutes later which means he left his house at 6.40am.I also know that Shamus was traveling 3 times faster than Grace.
I need to know the speed of Grace to solve the problem.
Grace traveling at a speed of 5m/s would be a reasonable number.So if Grace was traveling at 5m/s, Shamus would be traveling at 15m/s.
The time Shamus left home,
Grace travelled 5m/s X 600=3000m
15m/s - 5m/s = 10m/s
3000m÷10=300s=5mins
Q1)Shamus caught up at 6.45am
Distance covered by Shamus is 15 x 300s=4500m
4500m>800m
Q2)Shamus would not be able to catch with Grace.

5. I know that Grace left home at 6.30 am and her brother Shamus left home at 6.40 am. We also know that the speed of Shamus on his bicycle is 3 times as fast as Grace.
I need to know Grace’s speed. A possible number is 1 m/s. If Grace’s speed is 1 m/s, Shamus’ speed will be 3 m/s.
10 mins = 600 s
So, by the time Shamus leaves home, Grace will already be 600m from home.
Q1: 3 m/s - 1 m/s = 2 m/s
600m / 2m/s = 300s
300s = 5 mins
ANS: Shamus caught up with Grace at 6.45 am.

Q2: The amount of time between the time Grace left home and the expected time Shamus will catch up is 15 mins.
The distance Grace can travel in 15 mins: 1m/s x 900s = 900m
But the distance from home is only 800m.
So, Shamus will not be able to reach Grace before she arrives at school.

6. what i know:
>grace left at 6.30
>shamus left home at 6.40
>shamus is travelling 3 times faster
what i need to know:
>what is each of their speed
reasonable assumption:
>Grace travelling at 1m/s
>shamus is travelling at 3m/s
Q1:
Understanding-> Grace has already travelled some diastance before shamus started his journey and therefore she gained time on him, however after shamus started his journey he was gaining time on grace because he was faster.
Things that need to be "clarified":
>Distace Grace travelled in 10minutes
>How much Shamus was gaining on Grace
>division of the above two
Solution:
1m/s X 10m = 600s
3m/s - 1m/s = 2m/s
600s/2m/s = 5mins

Q2:
Understanding:
As figured out in the previous part the time shamus took to reach grace was at 6.45. If Grace had reach school by that time Shamus would have not been able to reach Grace.
Things to be "clarified":
>Time Grace was travelling before Shamus reached he
>whether the distance(above) has exceeded 800m
Solution:
6.45am - 6.30am = 15mins
1m/s X 15mins = 900m
900m exceeds 800m
No, Shamus did not reach in time(ANSWER)

7. What I know:
I know that Grace left home at 6.30am and that Shamus left home at 6.40am. Shamus is travelling at a speed 3 times that of Grace's.

The information I need:
The speed Grace is travelling at.

The solution:
The speed Grace is travelling at could be 1m/s
The speed Shamus is travelling at will then be 3m/s

When Shamus left the house, Grace traveled -> 600 x 1 = 600m
Time needed for Shamus to catch up -> 3m/s - 1m/s = 2m/s
600m divided by 2m/s = 300s
300s = 5mins
Shamus caught up with Grace at 6.45am
900 x 1m/s = 900m
The school is 800m from home and Grace had enough time to travel 900m before Shamus caught up so Shamus did not catch up with her.

8. I know that Grace left the house at 6.30a.m. and Shamus left the house at 6.40a.m. I also know that Shamus' bicycle is 3 times faster than Grace.

I need to know the speed that Grace is traveling at.

1 m/s is a reasonable number.

Q1
Grace left the house at 6.30a.m. and kept walking for 10 mins.
10 min x 1m/s(60m/min) = 600m
She travelled 600m.

Shamus left the house at 6.40a.m. In order to catch up, he will need to cover 600m.

In one minute:
Grace covers 60m and Shamus covers 180m
Shamus covers 120m more than Grace in 1 min.
600m/120m=5
Shamus needs 5 mins to catch up with Grace.

Shamus caught up with Grace at 6.45a.m.

Q2
5minx180m/min=900m
In 5 mins, Shamus has covered 900m.

Since the school is 800m away, Shamus will not catch up with Grace on time.

9. Since i don't know Grace's speed i'll take it as 1m/s and since Shamus' speed is 3 times of hers. That will put him at 3m/s

Q1.Since Grace left earlier by 10 mins the distance between them would be:10X60X1=600m
and the difference in their two speeds is:3m/s-1m/s=2m/s
2m/s would be the catchup rate.
Sothe time taken to catch up would be:600m÷2m/s=300s=5mins
Grace left the house at 6.30a.m. while Shamus left at 6.40 and needed 5 mins to catch up which means he catch up at 6.45a.m.

Ans:6.45 a.m.
Q2.Grace takes this amount of time to reach the school: 800m÷1m/s=800s=13 1/3 mins
which means she reaches at 06:43:20
while Shamus only catches up to her at 06:45:00

Ans:No,He is unable to catch up to her on time.

10. [Assuming that Grace's speed is 1m/s and Shamus' speed is 3m/s]
1 m/s x 600 = 600m
600/2 = 300s
0630 + 10min + 5min = 0645
*Shamus will catch up with Grace at 0645.
300 x 3 = 900m
900m is more than 800m which is the distance of Grace's school from her home. Therefore...
**Shamus will not be able to catch up with his sister before she reaches school.

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12. What I know:
- Grace left home at 6:30am
- Shamus left home at 6:40am
- Shamus's speed to Grace's speed is 1:3

I need to know Shamus' and Grace's speed
Assume Shamus's speed is 1m/s, thus Grace's speed must be 3m/s

Q1: 10min = 600s
1m/s x 600s = 600m (The distance between Grace and Shamus)
3m/s - 1m/s = 2m/s (Speed difference between Grace and Shamus)
600m ÷ 2m/s = 300s (Time difference between Grace and Shamus)
300s = 5min
6:30am + 10min + 5min = 6:45am

Ans: Shamus caught up with Grace at 6:45am

Q2: 300s x 3m/s = 900m

The distance from home to school to is 800m but the distance
needed to catch up with her is 900m. This means that Shamus will
not be able to catch up with her before she reaches school.

13. What I know:
Grace left home at 6.30 am
Shamus left home at 6.40 am.
Their difference in time is 10 minutes.
Shamus's speed to Grace's speed is 3:1
Their difference in speed is 2 units.

What I need to know:
Grace's speed and distance from home in the 10 minutes.

Assuming Grace's speed is 1m/s,
Q1: What time was it when Shamus caught up with Grace?
Grace:
T=10 minutes
=600s
S=1m/s
D=600s X 1m/s
=600m (Grace's distance from home in the 10 minutes)

Shamus catch up:
D=600m
S=2m/s (difference in speed)
T=600m÷ 2m/s
=300s
=5 minutes (time needed to catch up)

6.30 am + 10 minutes + 5 minutes
= 6.45 am
Shamus caught up with Grace at 6.45 am.

Q2: If the school is 800m from home, did Shamus reach Grace before she arrived at school?
Total time difference: (10+5) minutes
=15 minutes
Grace:
T=15 minutes
=900s
S=1m/s
D=900m (home to school only 800m apart)
--> Grace has already arrived at school by the time Shamus caught up with her.
Shamus will not be able to catch up with her before she arrives at school.

14. What information do you know from the problem?
Grace left home at 6.30 am.
10 mins later his Shamus left to pass Grace her wallet
Shamus left home at 6.40 am.
Shamus travelled 3 times faster to catch up
What else do you need to know to solve the problem?
Grace walking speed
Pick a reasonable number for the information you need.
1m/s

Q1: What time was it when Shamus caught up with Grace?
Grace speed: 1m/s
Shamus speed: 1m/s x 3 = 3m/s
In 10mins, Grace travelled:
1min = 60s
10min = 600s
1m/s x 600s = 600m.
So we know when Shamus left home, Grace already travelled 600m
3m/s - 1m/s = 2m/s
Shamus is closing the gap between them by 2m/s
600m ÷ 2m/s = 300s
300s = 5min
So, Shamus took 5min to catch up
6.40 am, 5mins later => 6.45am.
Shamus caught up with Grace at 6.45 am.

Q2: If the school is 800m from home, did Shamus reach Grace before she arrived at school?
We can see that Grace walked for 15mins before Shamus caught up with her.
15mins = 900s
1m/s x 900s = 900m
Grace travelled 900m before Shamus caught up with her. But her school is 800m away. So, she have already reached her school.
Shamus did not reach Grace before she arrived at school.

15. What i know is that:
Grace left home at 6.30am.
After 10 min shamus went on his bike, three times faster than grace, to give her, her wallet, which means he left home at 6.40am.

What do i have to know is :
What is grace's and shamus' speed?

qn 1 :

Let's assume grace speed is 1m/s and shamus speed is 3m/s.

10min=600s

600x1=600m

3-1=2
600/2= 300s
300s= 5min
5min after 6.40am is 6.45 am.
Shamus caught up with him at 6.45am.

qn 2:

So it means that grace has been already walkin fo r15mins before shamus caught up with her.
So..
15mins= 900s
900x1= 900m.. Which means grace already arrived at school.

So, Shamus did not reach the school before Grace.

16. What i know:
Grace left home at 6.30pm
Shamus went after her at 6.40pm
His speed was 3 times faster than Grace.

What i have to know:
Grace's Speed
Shamus's Speed

Question 1:
Assuming Grace's speed is 2m/s
and Shamus's speed is 6m/s

10minutes = 600seconds

600 x 2m/s = 1200m
Grace would've traveled 1200m

Shamus needed to travel 1200m to catch up with her.
6m/s ( Shamus's Speed ) - 2m/s ( Grace's Speed )
= 4m/s ( The extra distance that Shamus covers )
1200m ÷ 4m/s = 300seconds
300seconds = 5minutes
6.40 + 5minutes = 6.45am//

Question 2:
Grace travels 1200m in 10minutes...
So, even before Shamus starts to go after her she is already at School.

Shamus would not be able to catch up with Grace

17. Qn 1.
Let's take it that Grace travels 1 m/s. It is only 10 minutes after she left the house at 6.30am that Shamus found Grace's wallet and started to go after her, so Shamus left at 6.40am, 10 minutes after 6.30.
To calculate how far Grace had travelled by then, we first find the number of seconds in 10 minutes, so 60x10, which gives us 600 seconds. Grace travels at 1 m/s, so she has travelled 600m in the 10 minutes.
Shamus travels 3 times faster than Grace, so he travels at 3 m/s. He can gain 2m with every second, so 600 divided by 2 is 300, giving 300 seconds.
300 seconds = 5 minutes
6.40 + 5 mins = 6.45 am

Q2. Within 10 minutes, Grace would have travelled 1200m, way overshooting the 800m mark. Therefore, Grace would have reached school before Shamus, even before he left the house.

18. Q1:
I will assume Shamus’ speed is 3m/s and Grace’s 1m/s.
10mins = 600seconds
1m/s x 600s = 600m (the distance Grace travelled within 10mins therefore also the distance Shamus need travel to catch up with Grace)
3m/s - 1m/s = 2m/s (Since the difference of speed between both of them is 2m/s, Shamus will be 2m closer to Grace each second)
600m ÷ 2m/s = 300s
300s = 5mins
0640 + 5 = 0645

It would be 0.45am when Shamus caught up with Grace.

Q2:
When Shamus caught up with Grace, it would be 15 minutes after she left home.
15mins = 900s
1m/s x 900s = 900m (the distance Grace would have covered in 15 mins)
The school is only 800m away from home so Grace would have reached school before Shamus caught uo with her.

19. What i know:
Grace left home at 6.30pm
Shamus left home at 6.40pm
Shamus' speed was 3 times faster than Grace.
Assuming that Grace's speed is 1m/s and Shamus' speed is 3m/s
1 m/s x 600 = 600m
3m/s-1m/s=2m/s
600m/2m per s = 300s
0640+5= 0645
*Shamus will catch up with Grace at 0645.
300s x 3=900s
1m/s x 900s
900m is more than 800m.
Therefore, Grace will reach school before Shamus does.

20. I know that Grace left the house at 6.30a.m., Shamus at 6.40 a.m.
Shamus was 3 times faster than Grace. If Grace's speed was 1m/s, Shamus would be 3m/s. Hence
1m/s x 600 = 600m
3m/s - 1m/s = 2m/s
600m/2m per s = 300s
Shamus will catch up with Grace at 6.45 a.m.
6.30 a.m. - 6.45 a.m. = 15min
15min= Grace walking 900m (1m/s x 900)
Grace will reach school before Shamus

21. 1)
I know that Grace left home at 6.30am, Shamus found her wallet at 6.40am, and he traveled 3 times as fast as Grace. I need to know Grace's speed in order to solve the problem. A reasonable number would be 1m/s.
Shamus's speed would then be 1m/s x 3= 3m/s
The distance Grace covered= 1m/s x 10mins = 600m
3m/s-1m/s=2m/s
600m/s/2= 300s=5min
5min after 6.40am is 6.45am
Ans: 6.45am
2)I know that the school is 800m from home.
6.30am to 6.45am is 15mins.
1m/s x 15mins=900m
900 had exceeded 800m, hence Shamus did not reach Grace in time

22. 1) I know Grace left at 6.30am and Shamus left at 6.40am.
I know Shamus traveled three times faster than Grace.
I need to know Grace's speed.

A possible speed for Grace could be 1m/s.
Hence, Shamus would be traveling at 3m/s
10 minutes=600 seconds
Distance covered by Grace= 1m/s x 600s = 600m
3m/s - 1m/s = 2m/s
600m÷2m/s =300s = 5min
5 min after 6.40am is 6.45am

2) 6.30am to 6.45am is 15 min
1m/s x 15min = 900 m
Shamus had not reached Grace in time.

23. What I Know

1) Grace left home at 6.30 am to walk to school.

2)At 6.40 am her brother Shamus rode after Grace.

3)Shamus rode his bicycle 3 times as fast as Grace walked.

What I need to know

Either the speed of Grace or Shamus (preferably both)

Q1) A reasonable speed for Grace will be 1m/s and thus the speed for Shamus will be 3 m/s

Dist Covered by Grace before Shamus left --> [1 x ( 10 x 60 ) ] = 600m

Shamus left 10 minutes after Grace . So by the time Shamus left,
Grace will have walked 600m

Difference in speed between Shamus and Grace --> 3m/s-1m/s = 2m/s

600m ÷ 2m/s = 300s
= 5min

5 minutes after 6.40 am is 6.45 am

Shamus would have caught up with Grace at 6.45 am

Q2) 6.30 to 6.45 --> 15 mins

1m/s x ( 15x 60 ) = 900 m

Grace would cover 900m by the time he catches up with Grace but the distance to school is only 800m so , Shamus would not have catched up with Grace on time.