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Math Help - Speed, distance etc

  1. #1
    Member GAdams's Avatar
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    Speed, distance etc

    Fred cycled from home to his friends house and back again.
    The distance is 20km.
    On his way home, he cycled x km per hour.
    On his way back, his speed decreased by 2km per hour.
    It took him 4 hours altogether to cycle to his friends house and back.

    1. Write down an equation for x

    x = (20/4) - 2 ?

    2. Show that the equation can be written as x^2 - 12x + 10 = 0
    3. Solve the equation in question 2 to 1 decimal place
    4. Only one of teh answers in question 3 can be Freds speed. Explain why.
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  2. #2
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    Quote Originally Posted by GAdams View Post
    Fred cycled from home to his friends house and back again.
    The distance is 20km.
    On his way home, he cycled x km per hour.
    On his way back, his speed decreased by 2km per hour.
    It took him 4 hours altogether to cycle to his friends house and back.

    1. Write down an equation for x

    x = (20/4) - 2 ?

    2. Show that the equation can be written as x^2 - 12x + 10 = 0
    3. Solve the equation in question 2 to 1 decimal place
    4. Only one of teh answers in question 3 can be Freds speed. Explain why.
    Hello,

    you know that speed = \frac{distance}{time} that means time = \frac{distance}{speed}

    So you can set up an equation to calculate the time:

    \frac{20}{x} + \frac{20}{x-2} = 4 . Multiply both sides by x(x-2):

    20(x-2) + 20x = 4x(x-2)

    20x - 40 + 20x = 4x^2 - 8x

    4x^2 - 48x + 40 = 0

    x^2 - 12x + 10=0

    I assume that you know how to solve a quadratic equation. (I've got the solutions: x =11.1 or x = 0.901) It is obvious that the 2nd solution never satisfies the given conditions because Fred would have traveled back with a negative speed
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  3. #3
    Member GAdams's Avatar
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    I tried using the formula to solve it because I didn't think it could be factorised, bt got different answers:

    x = ( -12 + or - sq.rt 12^2 - 4*1*-10 ) / 2

    x = ( -12 + or - sq.rt 184 ) / 2

    x= -5.22 or -18.78

    Arghhhh!
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  4. #4
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    Quote Originally Posted by GAdams View Post
    I tried using the formula to solve it because I didn't think it could be factorised, bt got different answers:

    x = ( -12 + or - sq.rt 12^2 - 4*1*-10 ) / 2

    x = ( -12 + or - sq.rt 184 ) / 2

    x= -5.22 or -18.78

    Arghhhh!
    Hello,

    you are one sign away from the corect solution:

    x = ( 12 + or - sq.rt (12^2 - 4*1*10 )) / 2

    x = ( 12 + or - sq.rt 104 ) / 2

    x= 11.1 or 0.901
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