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Math Help - Brain Thinkers

  1. #1
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    Brain Thinkers

    Could I please have some help with these 2 questions?
    1. In a maths competition with 15 questions, 6 marks are given for each correct answer, 0 marks for each wrong answer and 3 marks for no answer. Bill scored 51 points in the competition. What is the greatest number of wrong answers he could have had.
    2. A bi-athlete travels 30km in 2.25 hrs. She cycles part of the way at 20 km/h and runs the rest at 8 km/h. How far did she run?
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by not happy jan View Post
    Could I please have some help with these 2 questions?
    1. In a maths competition with 15 questions, 6 marks are given for each correct answer, 0 marks for each wrong answer and 3 marks for no answer. Bill scored 51 points in the competition. What is the greatest number of wrong answers he could have had.
    2. A bi-athlete travels 30km in 2.25 hrs. She cycles part of the way at 20 km/h and runs the rest at 8 km/h. How far did she run?
    (2) Let t = #hrs cycling

    Let 2.25 - t = #hrs running

    Total distance = 30 km

    D = rt

    Distance is constant at 30

    20(t) + 8(2.25 - t) = 30

    20t - 8t + 18 = 30

    12t = 12

    t = 1 hours cycling

    Number of hours spent running = 2.25 - 1 = 1.25 hours running

    D = 8(1.25) = 10 km running

    D = 20(1) = 20 km cycling
    --------------------------------------
    Total = 30 km
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  3. #3
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    Hello, not happy jan!

    2. A bi-athlete travels 30km in 2.25 hrs.
    She cycles part of the way at 20 km/h and runs the rest at 8 km/h.
    How far did she run?
    We will use: . \text{Distance} \:=\:\text{Speed} \times \text{Time} \quad\Rightarrow\quad T \:=\:\frac{D}{S}


    Let x = distance she ran.
    Then 30-x = distance she cycled.

    She ran x km at 8 km/hr.
    . . This took her: . \frac{x}{8} hours.

    She cycled 30-x km at 20 km/hr.
    . . This took her: . \frac{30-x}{20} hours.


    Her total time was 2\tfrac{1}{4} hours.

    There is our equation! . . . \frac{x}{8} + \frac{30-x}{20} \:=\:\frac{9}{4}

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