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Math Help - Problem Solving- Travel (Time is of the essence here...)

  1. #1
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    Problem Solving- Travel (Time is of the essence here...)

    "Jim and Freda live 3 miles apart. They both leave their houses at the same time and walk to meet each other. Jim walks at 2.5 miles/hour and Freda walks at 3.5 miles/hour. How far will Jim walk before he meets Freda?

    Please post a thorough response showing all the steps so I understand! Thank you in advance.
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  2. #2
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    Hello, Mac Addict!

    Here's a back-door solution . . .


    Jim and Freda live 3 miles apart.
    They both leave their houses at the same time and walk to meet each other.
    Jim walks at 2.5 miles/hour and Freda walks at 3.5 miles/hour.
    How far will Jim walk before he meets Freda?

    They have a combined speed of: . 2.5 + 3.5 \:=\:6 mph.

    To cover 3 miles at 6 mph, it will take them a half-hour.

    In that time, Jim has covered: . \tfrac{1}{2} \ \times 2\tfrac{1}{2} \:=\:1\tfrac{1}{4} miles.


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    Assuming that we must use algebra . . .


    We will use: . }" alt="\text{(Distance)} \:=\:\text{(Speed)} \times \text{}" />

    Let t = time for them to meet (in hours).


    Jim walks at 2.5 mph.
    In t hours, he walks: 2.5t miles.

    Freda walks at 3.5 mph.
    In t hours, she walks: 3.5t miles.

    Together, they cover 3 miles: . 2.5t + 3.5t \:=\:3

    . . Then: . 6t \:=\:3\quad\Rightarrow\quad t \:=\:\tfrac{3}{6} \:=\:\tfrac{1}{2} hour.


    In that time, Jim walked: . \tfrac{1}{2} \times 2.5 \:=\:1.25 miles.

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