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Math Help - Distance and Speed related word problem

  1. #1
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    Distance and Speed related word problem

    Hey there. I have a word problem here, I think this is the right place to post. I am trying to get back into understanding algebra but I ran into a word problem that I can not begin to think of a formula able to solve that D=R*T can't. I guess I need help understanding how to formulate the problem;

    A freight train left Washington traveling
    east 7.8 hours before a diesel train. The
    diesel train traveled in the opposite direction
    going 17.1 mph slower then the freight train
    for ten hours after which time the trains
    were 941 mi. apart. How fast did the freight
    train travel?

    Your attention is greatly appreciated. Thank you!
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  2. #2
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    Re: Distance and Speed related word problem

    You can use D = rt here.

    For example, suppose the freight train traveled at r mph for 17.8 hours (because it traveled for 7.8 hrs, then another 10 hrs). Then the diesel train traveled at r - 17.1 mph for 10 hours. We can add their distances because the trains are in the opposite direction:

    17.8r + 10(r - 17.1) = 941

    Solve for r.
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  3. #3
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    Re: Distance and Speed related word problem

    Thank you very much! It makes a lot more sense now.
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  4. #4
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    Re: Distance and Speed related word problem

    Quote Originally Posted by richard1234 View Post
    You can use D = rt here.
    For example, suppose the freight train traveled at r mph for 17.8 hours (because it traveled for 7.8 hrs, then another 10 hrs). Then the diesel train traveled at r - 17.1 mph for 10 hours. We can add their distances because the trains are in the opposite direction:
    17.8r + 10(r - 17.1) = 941
    Solve for r.
    Disagree; 941 is not the distance travelled: it is distance that the 2 trains are apart...
    (or did I miss something?):

    F(@f mph)-------------->[17.8 h].....(941 miles).....[10 h]<-------(@f-17.1 mph)D

    Let freight train speed = f and total distance between the 2 starting points = x

    x - 17.8f - 10(f - 17.1) = 941 ; simplifies to x = 27.8f + 770 [1]

    You can now use any speed for f (greater than 17.1); say 100, then:
    [1] x = 27.8(100) + 770 = 3550 miles.

    Diesel's speed will be 100 - 17.1 = 82.9
    Distance = 82.9(10) = 829

    1780 + 829 + 941 = 3550

    So for unique solution, more information is required
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  5. #5
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    Re: Distance and Speed related word problem

    Yes, it is possible to interpret the problem in such a way that cannot solve it! It is also possible to interpret in such a way that we can and that makes much more sense. We are told that "A freight train left Washington" going east and that later a diesel left in the opposite direction. Although it is not said explicitely that language certainly implies that the diesel also left from Washington. It simply makes no sense to assume that the diesel left from some competely undisclosed location.
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  6. #6
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    Re: Distance and Speed related word problem

    Re-read original...agree with you; guess I'm too used to these being 2 "things" starting from different locations...
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  7. #7
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    Re: Distance and Speed related word problem

    I worked out richard1234's equation and it works out to r=40.32~ mph. The answer key states it is just 40 mph. I'm wondering if the 40.32 answer is correct but just asks to round off (40).

    Thank you guys for giving your deliberations.
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  8. #8
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    Re: Distance and Speed related word problem

    You should get exactly 40 mph right off the bat.
    f - freight train speed

    f(10 + 7.8) + 10(f - 17.1) = 941
    10f + 7.8f + 10f - 171 = 941
    27.8f = 1112
    f = 40
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  9. #9
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    Re: Distance and Speed related word problem

    Yeah, I got exactly 40.
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