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Math Help - Word Problem - Car Travel

  1. #1
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    Word Problem - Car Travel

    A car travels from one town to another at a speed of 32mph. If it had gone 4 mph faster, it could have made the trip in 1/2 hr less time. How far apart are the towns?

    So far I have rate of 32mph, 32+4
    x = initial time
    y = x-1/2

    Please help.
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  2. #2
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    Quote Originally Posted by mcruz65 View Post
    A car travels from one town to another at a speed of 32mph. If it had gone 4 mph faster, it could have made the trip in 1/2 hr less time. How far apart are the towns?

    So far I have rate of 32mph, 32+4
    x = initial time
    y = x-1/2

    Please help.
    speed= distance/time so, letting d be the distance between the two towns, in miles, and t be the time, in hours, for the trip, 32= d/t.

    If "it had gone 4mph faster" its speed would have been 32+ 4= 36 and "it could have made the trip in 1/2 hr less time" so the time would be t- 1/2. Now "speed= distance/time" so 36= d/(t+1/2).

    32= d/t is the same as d= 32t.
    36= d/(t+1/2) is the same as d= 36(t+1/2)= 36t+ 18.

    d= 32t= 36t+ 18.

    Solve 32t= 36t+ 18 for t and then use d= 32t to find the distance between the towns.
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  3. #3
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    Word Problem - Car Travel

    Ok this is what I have so far.

    32t = 36t + 18
    -36t + 32t = 18
    -4t = 18

    -4t/-4 = 18/-4
    t= -4.5

    d=32t
    d=32(-4.5)
    d= -144 I don't understand why the answer is negative. Where did I go wrong?
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  4. #4
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    Shouldn't it be 36 = d/(t-1/2), as it takes less time at a higher speed?
    Which leaves you with an answer of t = 4.5
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  5. #5
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    Word Problem - Car Travel

    So you are saying that the equations should be like this.

    36t = 32t + 18
    36t - 32t = -32t + 18
    4t = 18
    4t/4 = 18/4
    t = 4.5

    d=32t
    d=32(4.5)
    d=144

    Is this correct?
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  6. #6
    Member alexgeek's Avatar
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    Hmm that looks overly confusing, mine was like:
    32 = \frac{d}{t}
    d = 32t

    36 = \frac{d}{t-\frac{1}{2}}
    d = 36(t-\frac{1}{2}) = 36t - 18

     \therefore 32t = 36t - 18
    -4t = -18
    t = \frac{-18}{-4} = 4\frac{1}{2}

    Then obviously sub into d=32t like you have done to get 144.

    36t - 32t = -32t + 18
    Does not simplify to 4t = 18, the -32t on each side would cancel to leave 36t = 18 so you've gone wrong somewhere.
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  7. #7
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    Let t = time in minutes

    (32mph)(t)= (36 mph)(t-30)

    32t= 36t- 1080

    -4t= -1080

    t= 270 minutes

    270 minutes

    (32 miles/hour)/(60 min) = .533333 miles/min

    (.533333 miles/min)(270 min) is about 144 miles
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