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Anyone Know How To Solve This Problem?

  1. Jan 26, 2004 #1
    The question is:

    A person takes a trip, driving with a constant speed 89.7 km/h except for a 21.5 min rest stop.
    If the person's average speed is 70.9 km/h, how far is the trip? Answer in units of km.

    I haven't done this kind of thing for years!! and I was just wondering if I solved it properly.. here is what i came up with.....

    time = 89.7 x (t - 21.5/60) = 70.9, 89.7 t - 38.5 = 70.9 t, t = 2.70 h

    distance = 70.9 x 2.70 = 191.43 km

    Is that right? Any help would be greatly appreciated.

  2. jcsd
  3. Jan 26, 2004 #2
    Let d be the length of the trip (km). Let t be the time of the trip (hours).

    70.9t = d
    89.7(t - 21.5/60) = d
    70.9t = 89.7t - 1928.55/60
    18.8t = 1928.55/60
    t = 1.71
    d = 70.9t = 121

    The trip was 121 km long and took 1.71 hours.
  4. Jan 27, 2004 #3
    i wish i knew how you did that...

    but i don't even know what / <-- means?

    i think it means to divide but i've forgotten all of the math i was taught.

    it's been years.
  5. Jan 27, 2004 #4


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    Okay, heres a "translation".

    As Tron3k said "Let d be the length of the trip (km). Let t be the time of the trip (hours)."

    Since the person stopped for 21.5 min.= 21.5 min/60 min/h (21.5 divided by 60)= 0.358 h, the time actually in motion (at a constant speed of 89.7 km/h) was t- 0.358 hours. Since speed is defined as "distance divided by time" we have 89.7= d/(t-0.358) or (multiply by t-0.358 to get rid of the fraction) 89.7(t-0.358)= d.

    We are told that the average speed (averaging the constant 89.7 when he was moving with the 0 speed while stopped) was 70.9 km/h.
    The average speed is calculated (again using "distance divided by time") using the total time: 70.9= d/t or d= 70.9t.

    Since d is the same in both equations, d= 70.9t= 89.7(t- 0.358)=
    89.7t- (89.7)(0.358)= 89.7t- 32.15 or
    70.9t= 89.7t- 32.15

    Subtract 89.7t from both sides: -18.8t= -32.15. Now divide both sides of the equation by -18.8: t= -32.15/-18.8= 1.71 hours.
    (Much to my amazement, the same answer Tron3k got!)

    Now put that back into either d= 89.7(t- 0.358) or d= 70.9t:
    Since d= 70.9t is easier: d= 70.9(1.71)= 121 km.
  6. Jan 27, 2004 #5

    hahaha rofl :wink:
  7. Feb 6, 2011 #6
    I wanted to ask how you got 18t?
  8. Feb 7, 2011 #7


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    ??? What "18t"? I did get "18.8t" exactly like I said:

    70.9t- 89.7t= (70.9- 89.7)t= -(89.7- 70.9)t= -18.8t.
    That made the equation -18.8t= -32.15 so I multiplied both sides by -1:

    18.8t= 32.15.

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