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Math Help - Rational Expressions

  1. #1
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    Rational Expressions

    I have been trying a couple problems for the past hour and am having a hard time.
    Could someone please walk me through each, or even one of the problems?
    If you solve it could you please show work so I can learn?
    Thank you so much!

    1. A family travels 18 miles downriver and returns. It takes 8 hours to make the round trip. Their rate in still water is twice the rate of the current. How long will the return trip take?

    2. The circumference of a circle varies directly as the diameter. A circular pizza pie with a diameter of 1 foot has a circumference of 3.14 feet. What will be the circumference of a pizza pie with a diameter of 1.5 feet?
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  2. #2
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    Quote Originally Posted by Ravangerz View Post
    1. A family travels 18 miles downriver and returns. It takes 8 hours to make the round trip. Their rate in still water is twice the rate of the current. How long will the return trip take?
    So 8 hours in total, as the rate is twice as much on the return (r) as the downriver part (d) then 2r=d and 8 = r+d \implies 8=r+2r \implies r = \frac{8}{3}

    Quote Originally Posted by Ravangerz View Post

    2. The circumference of a circle varies directly as the diameter. A circular pizza pie with a diameter of 1 foot has a circumference of 3.14 feet. What will be the circumference of a pizza pie with a diameter of 1.5 feet?
    C\propto d \implies C=kd and d=1 when C=3.14 solve for k when 3.14 = k\times 1
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  3. #3
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    Ahh got it
    thanks alot!
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