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Homework Help: Average speed with an unknown distance

  1. Mar 5, 2008 #1
    [SOLVED] Average speed with an unknown distance

    You travel from Place A to Place B, half the time at a speed of 60km/h and the other half at 100km/h. On the return journey, you travel half the distance at 60km/h, and the other half at 100km/h.

    a) What is your average speed from A to B?

    b) What is your average speed from B to A (return journey)?

    c) What is your average speed for the entire trip?



    a) [tex]\overline{Sp}[/tex] = (60 + 100)/2 = 80km/h... Easy enough.


    b&c)
    I just don't know where to start with this.
    I tried a displacement vs. time graph but without any actual values for the displacement I didn't know what to do.

    I'm not necessarily after an answer for this, but a nudge in the right direction would be greatly appreciated.

    Thanks,
    Yorick.
     
  2. jcsd
  3. Mar 6, 2008 #2
    Okay so I've been playing around a bit more, substituting values for displacement.

    This is for b)

    Letting x=100km,
    I travel 50km @ 60km/h = 50min = 5/6 h
    and 50km @ 100kmh/h = 30min = 1/2 h

    Then [tex]\bar{Sp}[/tex] = Distance travelled / (t[tex]_{2}[/tex] - t[tex]_{1}[/tex]) right?

    So t2 would be 5/6 + 1/2, t1=0

    then [tex]\bar{Sp}[/tex] = 100 / (4/3)
    =75 km/h




    Let x=200km
    100km @ 60km/h = 100min = 10/6 h
    100 km @ 100km/h = 1 h

    then [tex]\bar{Sp}[/tex] = 200 / (16/6)
    =75km /h

    Valid reasoning?
    PS sorry for bad Latexing, my subscripts came out as superscript so I gave up.
     
  4. Mar 6, 2008 #3
    Indeed, it is possible to calculate out .
    t= 1/2s/60 +1/2s/100= s/120+s/200
    v=s/t = s/(s/120+s/200) = 75km h^-1

    c) just easy , A->B = the same distance.
    you have the average speeds for both sides...
     
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