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Average speed

  1. Aug 23, 2010 #1
    1. The problem statement, all variables and given/known data

    Hi

    I read a question recently on the British Mensa website and I thought the answer was 112.5mph. The answer given was 108mph. What is the calculation for this scenario?

    "Lap 1 is completed at 135mph, lap 2 is completed at 90mph, what’s the average speed?"



    2. Relevant equations

    summation and division of two numbers


    3. The attempt at a solution

    135 plus 90 equals 225. 225 divided by 2 eqals 112.5


    Thanks.

    N.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 23, 2010 #2

    kuruman

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    Not in this case. Averaging is sometimes tricky. Average speed is defined as total distance traveled divided by total time required to travel that distance. Use this idea and you might be surprised with the result.
     
  4. Aug 23, 2010 #3
  5. Aug 23, 2010 #4

    kuruman

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    So? Can you do the calculation as I indicated? It requires a little bit of algebra or the realization that is question is entirely analogous to finding the equivalent resistance of two resistors in parallel or the equivalent capacitance of two capacitors in series.
     
  6. Aug 23, 2010 #5
    With this information I cannot. We only have two average speeds, one per lap (or two constant speeds, one per lap). We have neither a distance or a time.
     
  7. Aug 23, 2010 #6

    kuruman

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    Neither of these are needed. Just the knowledge that the laps are of equal length. Start writing something down and see what develops.

    Step 1. Can you write an equation for the definition of the average speed that I gave you? Use symbols for quantities that you don't know and have faith that it will all come out in the wash.
     
  8. Aug 23, 2010 #7
    If L = lap distance and T1 and T2 = time to travel each lap, we can write:

    Average speed = 4L / (T1 + T2)

    But I can't get further than this.
     
  9. Aug 23, 2010 #8

    kuruman

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    It should be

    vave = 2L/(t1+t2) where L is the distance of one lap. The total trip is two laps or 2L.

    Step 2: Can you find expressions for t1 and t2 in terms of L and v1 and v2?
     
  10. Aug 23, 2010 #9
    t1 = v1 / L

    t2 = v2 / L

    Vavg = 2L2 / (v1 + v2)

    = 2L2 / (135 + 90)

    = L2 / 112.5


    Where can I go from here?
     
  11. Aug 23, 2010 #10

    kuruman

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    No. t1 = L / v1 and t2 = L / v2.

    Step 3: Now add the two times together to get the sum. Be sure to add the fractions correctly on the right side. Replace the sum t1+t2 in the equation for vave and see what you get.
     
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