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Thread: distance speed problem

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    distance speed problem

    1. Pat biked 1 mile in 3 minutes with the wind at her back, and then she returned in 4 minutes riding against the wind. What was the speed of the wind?

    2. A fraction has a value or 3/4. If 7 is added to the numerator, the resulting fraction is equal to the reciprocal of the original fraction. Find the other fraction.
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    Senior Member Peritus's Avatar
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    $\displaystyle \left\{ \begin{gathered}
    \left( {v_{Pat} + v_{wind} } \right) \cdot t_1 = d \Rightarrow 3\left( {v_{Pat} + v_{wind} } \right) = 1 \hfill \\
    \left( {v_{Pat} - v_{wind} } \right)t_2 = d \Rightarrow 4\left( {v_{Pat} - v_{wind} } \right) = 1 \hfill \\
    \end{gathered} \right.
    $
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    Quote Originally Posted by sleigh View Post
    1. Pat biked 1 mile in 3 minutes with the wind at her back, and then she returned in 4 minutes riding against the wind. What was the speed of the wind?
    Let us say that Pat's natural speed (in the absence of wind) is $\displaystyle s$, and call the speed of the wind $\displaystyle v$. With the wind at her back, Pat would be traveling at a total speed of $\displaystyle s+v$, while she would be traveling at a speed of $\displaystyle s-v$ when against the wind.

    We are told that she initially bikes 1 mile in 3 minutes. So:

    $\displaystyle \text{total speed}=\frac{\text{distance}}{\text{time}}$

    $\displaystyle s+v = \frac{1\text{ mi}}{3\text{ min.}}$

    But on the trip back we have

    $\displaystyle s-v = \frac{1\text{ mi}}{4\text{ min.}}$

    Now, you solve two equations in two unknowns. Easy, right?

    Quote Originally Posted by sleigh View Post
    2. A fraction has a value or 3/4. If 7 is added to the numerator, the resulting fraction is equal to the reciprocal of the original fraction. Find the other fraction.
    Assign variables to represent the numerator and denominator, say $\displaystyle m$ and $\displaystyle n$, and note that the reciprocal of a fraction $\displaystyle \frac{a}{b}$ just means that the fraction should be "flipped" to be $\displaystyle \frac{b}{a}$.

    Set up your equations and show us your work if you get stuck; you should be able to do this one.
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