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Math Help - speed questions

  1. #1
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    speed questions

    I have three question I need help with:

    Over a distance of 120km, the average speed of a train is 40km/h faster than that of a car. If the train covers the distance in 30 min less time, find its average speed?

    To save fuel on the 240km trip to their cottage, the Nakumura family reduce their usual average speed by 20km/h. This lengthens the journey time by 1 h. What is the slower average speed?

    Car A leaves Toronto for Montreal, 500 km away, at an average speed of 80km/h. Car B leaves Montreal for Toronto on the same highway 2 h later at 100km/h. How far are they from Toronto when they pass?
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  2. #2
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    Quote Originally Posted by andrewpark2 View Post

    Over a distance of 120km, the average speed of a train is 40km/h faster than that of a car. If the train covers the distance in 30 min less time, find its average speed?
    Let the average speed in km/hr of the train be x, then the average speed of the car is x-40.

    Time for train to cover 120 km is 120/x hours

    Time for car to cover 120 km is 120/(x-40) hours

    So:

    \frac{120}{x-40} - \frac{120}{x}=0.5 hours

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by andrewpark2 View Post
    To save fuel on the 240km trip to their cottage, the Nakumura family reduce their usual average speed by 20km/h. This lengthens the journey time by 1 h. What is the slower average speed?
    Let the lower avaerage speed be x km/hr.

    The original time to complete the journey was 240/(x-20) hours

    The new time to complete the journey is 240/x hours

    So:

    \frac{240}{x}-\frac{240}{x-20}=1 hour

    RonL
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  4. #4
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    Quote Originally Posted by andrewpark2 View Post
    I have three question I need help with:

    Over a distance of 120km, the average speed of a train is 40km/h faster than that of a car. If the train covers the distance in 30 min less time, find its average speed?

    To save fuel on the 240km trip to their cottage, the Nakumura family reduce their usual average speed by 20km/h. This lengthens the journey time by 1 h. What is the slower average speed?

    Car A leaves Toronto for Montreal, 500 km away, at an average speed of 80km/h. Car B leaves Montreal for Toronto on the same highway 2 h later at 100km/h. How far are they from Toronto when they pass?
    Like others, I should have bypassed your question here for any of these two reasons:
    1) Too many problems in one posting or one thread. Like you really don't want to learn. Like you just want us to do your homework for you.
    2) You have posted 20 questions so far, yet you have not posted "Thanks" to anyone of those who replied to your previous 19 questions? They helped you but you did not even recognized their helping you?

    Anyway, since your 3 problems here are good for exercise to me, I will comment a little but I will not show the complete solutions.

    1.)Same distance, 120 km.
    Let rate of car = r
    Time to cover the 120 km = 120/r hrs.

    For the train:
    rate = r+40
    Time to cover the 120 km = (t -0.5) = (120/r -0.5) hrs.
    So, distance = rate*time,
    120 = (r +40)(120/r -0.5)
    Solve for r.
    Then the average speed of the train is (r +40) km/hr.

    ----------------------------
    2.) Same reasonings as part 1 above.
    240 = (r -20)(240/r +1)
    Solve for r.
    Then the slower speed is (r -20) km/hr

    ---------------------
    3) When cars A and B meets,
    A traveled (80)(2 +t), and B traveled 100(t), so,
    80(2 +t) = 100t
    t = 8 hrs

    That means when they met, A traveled 80(2 +8) = 800km
    and B traveled 100(8) = 800 km also.
    Since Toronto is 500km only away from starting line, then the two cars will not meet before Toronto. Meaning car A will reac Toronto before car B will show up minutes later.
    Last edited by ticbol; September 26th 2008 at 04:12 AM. Reason: I got mixed up myself.
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