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.

17 comments:

  1. Q1) Shamus' speed is 3 times of Grace's. So when Grace covers 3 times, Shamus covers in a minute. Grace now has a 10 minute start before Shamus, so we count onwards.

    Grace: 10, 11, 12, 13, 14, 15
    Shamus: 3, 6, 9, 12, 15.

    So Shamus will take 15 minutes to get to Grace. 15 minutes after 6:30am would be 6:45am. Thus, the answer's 6:45am.

    Q2) It honestly depends on Grace's speed.
    If we take 800m ÷ 15 minutes = 53.3 m/min (approx)

    If Grace walks faster than that speed, Shamus won't be able to catch up with her. But if Grace walks the same, or slower than that speed, Shamus will be able to catch up with her.

    ReplyDelete
  2. Q1) 6.45am

    Q2) Let's say Grace was travelling at 40m/min. If that is the case, then Shamus will be travelling at 120m/min.When Shamus left, Grace has already walked 400m. Since Shamus took 5 mins to catch up with Grace, he would have rode 600m. So he would be able to reach Grace.

    ReplyDelete
  3. Q1)Lets say Grace's speed is x meter/minute. After 10 minutes she would have travelled 10x meters. At that time, her brother left his house at a speed of 3 times faster than Grace, which is this case is 3x meter/ minute. Grace's brother is 2x meters/ minute faster than Grace since 3x-x. Grace is 10x meters faster so 10x/2x = 5.
    total time=10min+5min=15min
    15minutes after 6.30am is 6.45am.

    Answer=6.45am

    Q2) It would depend on her speed, because if Grace was travelling at 90m/minute, Her brother would be travelling at 270m/minute. That way, Grace would have already travelled 1350m before her brother catches up. It would be over 800m already, but at a slower speed, Grace's brother would have catch up before Grace reaches school.

    ReplyDelete
  4. Q1) 6.45a.m

    Q2) It would depend on graces speed. If grace had been traveling at 30m/min Shamus would have been travelling at 90m/min. This way he would have been able to reach grace in time.

    ReplyDelete
  5. 1)
    Since Grace's brother travels 3 times at fast as her, Grace would cover "x" distance in a minute. This means that her brother would travel "x" distance is a third of a minute. Thus, after 11 minutes of Grace walking, her brother would have travelled 3/11 of her distance. The answer is 6.45am.

    2) We would need to have a look at Grace's speed. If her speed is faster than 53m/min, her brother would not be able to catch up with her.

    ReplyDelete
  6. 1) Grace started her journey at 6.30a.m. Her brother started 10minutes later, thus, giving her a 10minute head start. However, Shamus's(her brother) speed is 3 times her speed. The answer is 6.45a.m.

    2) If Grace's speed increases, then Shamus won't be able to catch up. However, if her speed is constant or starts to slow down, then he will.

    ReplyDelete
  7. A1: Since Shamus went 3 times as fast as Grace, what Grace covered in 3 minutes, Shamus covered in a minute. Grace got a 10 minute head-start, and so, by the time Shamus had started, she had covered 10 minutes worth of distance. Shamus, traveling at 3 times Grace's speed, would catch up in (10 divided by 2) 5 minutes, where Grace would have taken 15 minutes to cover the same distance that shamus had covered in (15 divided by 3) 5 minutes. Therefore, Shamus would have caught up with Grace at 6:45am.

    A2: This answer depends on Grace's speed, but if Grace happened to be walking at the average human walking speed of 1.38 m/s or 82.8 m/min (Source: http://en.wikipedia.org/wiki/Walking), meaning that Shamus would be traveling at 248.4 m/min, Shamus would have caught up with Grace before school started.

    Working: 800m / 82.8m/min = 9.66min (approximately, to 2 S.F.)
    800m / 248.4m/min = 3.22min (approximately, to 2 S.F.)

    ReplyDelete
  8. 1) Shamus' speed is 3 times as fast as Grace, thus in every 3 minutes Grace covered, will be equivalent to 1 minute Shamus covered. So the time Shamus caught up with Grace is 6:45 am.

    2) It will depend on Grace's speed. If Grace's speed is 50m/min, so Shamus' speed is 150m/min. He will be able to catch up with her. However, if her speed is 60m/min, so his speed is 180m/min. He will not be able to catch up with her.

    ReplyDelete
  9. 1) Since Shamus' speed is 3 times of Grace,he would only need to cover 1 min for Grace's 3 mins. So the time when Shamus caught up with Grace is 6.45am.

    2)It depends on Grace's speed. If her speed was faster, her brother would not be able to catch up with her.

    ReplyDelete
  10. 1. Shamus' speed is 3 times faster than Grace's speed. So it will take 15 minutes for Shamus to catch up with Grace. So Shamus will catch up with Grace at 6.45am.
    Ans: 6.45am
    2. It depends on Grace's speed because if she increases her speed, Shamus will not be able to catch up with her but if she slows down, Shamus will be able to reach school before her.

    ReplyDelete
  11. 1.Sharmus speed is 3 times of Grace speed.To find Grace speed,the speed she is travelling at is from 11 and counting.To find Sharmus speed he is travelling in 3s.
    Grace 11,12,13,14,15
    Sharmus ,3,6,9,12,15

    They will need 15 minutes to meet each other.

    Ans:6.45

    2.It depend if it takes 10 minutes to reach the school Grace might have reach school before Sharmus left the house.By the time Sharmus found the wallet,Grace might be in school.

    ReplyDelete
  12. Shamus' speed is 3 times faster than Grace's speed. Hence every x distance traveled by Grace Shamus travel 3x distance.

    the lowest common multiple is 15 hence 15minutes after 6.30am is 6.45am

    Ans:6.45am


    2.if Grace travels at 50m/s Shamus travel at 150m/s. And it only took 5 minute for Shamus to reach Grace so it depends on the speed of Grace

    ReplyDelete
  13. 1)
    Grace: 10, 11, 12, 13, 14, 15
    Shamus: 3, 6, 9, 12, 15.

    Hence he will need 15 min to meet Grace.

    2) It will depend on Grace's speed. If Grace's speed is 50m/min, so Shamus' speed is 150m/min. He will be able to catch up with her. However, if her speed is 60m/min, so his speed is 180m/min. He will not be able to catch up with her.

    ReplyDelete
  14. Shamus travels 3x faster than Grace. Every x distance Grace travel, Shamus travels 3x distance.

    1) 6.45am

    2) Only if Grace travels at 50m/min. Shamus will travel at 150m/min.

    ReplyDelete
  15. Q1) 6.45am

    Q2)It will depend on how fast Grace walks to school.If it increases,Shamus will not be able to catch up with her.However,if her speed slows down or remains constant,then Shamus will be able to catch up

    ReplyDelete
  16. What time was it when Shamus caught up with Grace?
    Shamus caught up with Grace at 6:45am.

    If the school is 800m from home, did Shamus reach Grace before she arrived at school?
    It will depend on whether Grace's walking pace speeds up or slow down or speeds up and it also depends on whether her Brother's cycling speed slows down or remains constant or speeds up. Unless Grace's brother speeds up and Grace slows down, her brother may be able to catch up to her.

    ReplyDelete
  17. Q1)
    Grace: 11, 12, 13, 14, 15
    Shamus:3, 6, 9, 12, 15

    He needs 15 mins to catch up to her so it is 6:45 am

    Q2)
    It would have to see how fast does she travel at.
    If she was walking at a constant speed, Shamus would be able to catch up.

    ReplyDelete