Question 1155126
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Let d be the distance traveled <U>before lunch</U>, in miles.


Then the distance traveled after lunch is d-80 miles.


He spent {{{d/40}}} hours for the first part  and {{{(d-80)/50}}} hours for the second part.


The total time equation is


    {{{d/40}}} + {{{(d-80)/50}}} = {{{6}}}{{{1/2}}} hours = {{{13/2}}} hours.


To solve it, multiply both sides by 200. You will get

    5d + 4*(d-80) = 1300.


Simplify and find d.


    9d = 1620.

     d = {{{1620/9}}} miles = 180 miles.


Thus the partial distances are 180 miles and (180-80) = 100 miles, 

   and the total distance  is  180 + 100 = 280 miles.    <U>ANSWER</U>
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Solved.