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Math Help - Algebra - Speed, Distance Word Problem

  1. #1
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    Algebra - Speed, Distance Word Problem

    Any help with this one? Those are the equations I have below, yet still cannot seem to figure this one out.

    Jessica drove her car at a certain speed for the first 4 hours and increased its speed by 10 miles/hr, for the next two hours. If the total distance traveled by her was 500 miles, find the speeds at which Jessica drove her car at different times.

    V1 = D1 / T1

    V2 = V1 + 10

    T1 = 4
    T2= 2

    Ttot = T1 + T2 = 6

    Dtot= D1+D2 = 500

    Vavg = Dtot / Ttot = 83 1/3

    What I did was..

    [(V1+V2) / 2 ] = Vavg

    [((D1/4)+((D1/4)+10))) / 2 ] = Vavg

    Solved for D1 then solved for V1 and got 78 1/3. Checked my math and is correct.

    Is there any other way to solve this or did they just approximate in the answers?

    These are possible answers:

    80 and 90 miles/hr respectively
    60 and 80 miles/hr respectively
    50 and 60 miles/hr respectively
    Last edited by guest84; April 9th 2010 at 07:41 AM. Reason: Additional Info
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  2. #2
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    Quote Originally Posted by guest84 View Post
    Any help with this one? Those are the equations I have below, yet still cannot seem to figure this one out.

    Jessica drove her car at a certain speed for the first 4 hours and increased its speed by 10 miles/hr, for the next two hours. If the total distance traveled by her was 500 miles, find the speeds at which Jessica drove her car at different times.

    V1 = D1 / T1

    V2 = V1 + 10

    T1 = 4
    T2= 2

    Ttot = T1 + T2 = 6

    Dtot= D1+D2 = 500

    Vavg = Dtot / Ttot = 83 1/3

    What I did was..

    [(V1+V2) / 2 ] = Vavg

    [((D1/4)+((D1/4)+10))) / 2 ] = Vavg

    Solved for D1 then solved for V1 and got 78 1/3. Checked my math and is correct.

    Is there any other way to solve this or did they just approximate in the answers?

    These are possible answers:

    80 and 90 miles/hr respectively
    60 and 80 miles/hr respectively
    50 and 60 miles/hr respectively
    1. J. drove the car at a speed of v for 4 hours, that means she covered a distance of 4 v;
    then she drove the car at a speed of (v + 10) for 2 hours, that means she covered a distance of 2v + 20.

    2. Both distances must add up to 500:

    4v + 2v +20 = 500

    3. Solve for v.
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  3. #3
    Air
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    Quote Originally Posted by guest84 View Post
    Any help with this one? Those are the equations I have below, yet still cannot seem to figure this one out.

    Jessica drove her car at a certain speed for the first 4 hours and increased its speed by 10 miles/hr, for the next two hours. If the total distance traveled by her was 500 miles, find the speeds at which Jessica drove her car at different times.

    V1 = D1 / T1

    V2 = V1 + 10

    T1 = 4
    T2= 2

    Ttot = T1 + T2 = 6

    Dtot= D1+D2 = 500

    Vavg = Dtot / Ttot = 83 1/3

    What I did was..

    [(V1+V2) / 2 ] = Vavg

    [((D1/4)+((D1/4)+10))) / 2 ] = Vavg

    Solved for D1 then solved for V1 and got 78 1/3. Checked my math and is correct.

    Is there any other way to solve this or did they just approximate in the answers?

    These are possible answers:

    80 and 90 miles/hr respectively
    60 and 80 miles/hr respectively
    50 and 60 miles/hr respectively
    \text{Speed} = \frac{\text{Distance}}{\text{Time}} \implies \text{Distance} = \text{Speed} \times \text{Time}

    For the first four hours, she drives at an unknown speed, lets call it v_1. So using the formula:
    \text{Distance}_1 = 4v_1

    For the next 2 hours she drives at an increased speed. Lets call this v_2. So using the formula:
    \text{Distance}_2 = 2v_2

    But v_2 is 10 more than v_1.
    \text{Distance}_2 = 2(v_1+10)

    The total distance travelled is the combination of the distance traveled over the two times segments. We are given the total distance as 500 miles.
    \text{Distance} = \text{Distance}_1 + \text{Distance}_2
    500 = 4v_1 + 2(v_1+10)

    Solving for v_1 will give you the speed for the first four hours. Then using the fact given about how much the speed is increased, work out v_2 which is the speed for the next two hours.
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