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Math Help - D = rt

  1. #1
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    D = rt

    A truck travels 40 miles from point A to point B in exactly 1 hour. When the truck is halfway between point A and point B, a car starts from point A and travels at 50 miles per hour. How many miles has the car traveled when the truck reaches point B?
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  2. #2
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    Quote Originally Posted by symmetry View Post
    A truck travels 40 miles from point A to point B in exactly 1 hour. When the truck is halfway between point A and point B, a car starts from point A and travels at 50 miles per hour. How many miles has the car traveled when the truck reaches point B?
    "A truck travels 40 miles from point A to point B in exactly 1 hour...."
    That means the truck covers the 40 miles in 1 hour. []

    "...When the truck is halfway between point A and point B,..."
    That means at the halfway point, the truck spends 30 minutes after leaving A.

    "...a car starts from point A and travels at 50 miles per hour...."
    That means after the truck spends 30 minutes, the car starts leaving A at 40 miles per hour.

    "...How many miles has the car traveled when the truck reaches point B?"
    That means when the truck reaches point B, it spents the last 30 minutes of the 1 hour he can drive from A to B.
    So the car spents 30 minutes also by that time.
    d = rt,
    d = (50 mi/hr)(0.5hr) = 25 mi. ------------answer.

    -----
    30 minutes is half-hour, is 0.5hr.
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  3. #3
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    Quote Originally Posted by symmetry View Post
    A truck travels 40 miles from point A to point B in exactly 1 hour. When the truck is halfway between point A and point B, a car starts from point A and travels at 50 miles per hour. How many miles has the car traveled when the truck reaches point B?
    We need to find out how long it takes the truck to go half-way between A and B. The truck is moving (presumably) at a constant speed, so since it takes the truck an hour to move between A and B it must take it 1/2 hour to move half the distance.

    So how far has the car moved in this time?
    D = rt

    D = (50 \, mi/h)(1/2 \, h) = 25 \, mi

    -Dan
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  4. #4
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    ok

    I wish I could somehow learn to set up equations from word problem data.
    I've been struggling with word problems for years.

    I wonder how math people do it.

    Thanks!
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by symmetry View Post
    I wish I could somehow learn to set up equations from word problem data.
    I've been struggling with word problems for years.

    I wonder how math people do it.

    Thanks!
    It's a function of experience. I've done any number of similar problems in the past, so it was easy for me to set up. Perhaps you could start a "library" of solved word problems so you can look up how to do a similar problem when faced with a new one.

    -Dan
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  6. #6
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    ok

    I thank you very much.
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