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Algebra

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I have 2 questions in math that I am not quite sure about...

1. Mandy begins bicycling west at 30 mph at 11 A.M. If Liz leaves from the same point 20 min. later bicycling west at 36 miles per hour, when will she catch Mandy?

2. A mixture of 10% acid and 90% water is added to 5 liters of pure acid. The final mixture is 40% water. How many liters of water are in the final mixture?

thanks:)

  • Algebra -

    1. Write equations for distance traveled vs. the time after 11 AM. Set them equal and solve for t.
    M = .5 t (if t is in minutes)
    L = .6 (t -20)
    M = L when 0.5t = 0.6t -12
    0.1t = 12
    t = 120 minutes (after 11 AM), which is 1:00 PM

    2. Assume X liters of 10/90 mix are added
    Liters of acid in mix = 0.1X + 5
    Liters of water in mix = 0.9X
    Total volume of mix = 5 + X

    Solve 0.4 = 0.9X/(5+X)
    2 + 0.4X = 0.9X
    X = 4
    90% of X is the amount of water

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