Question 1185319
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Wilma drove at an average speed of 45 mi/h from her home in City A to visit her sister in City B. 
She stayed in City B 10 hours, and on the trip back averaged 50 mi/h. 
She returned home 48 hours after leaving. How many miles is City A from City B?
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Obviously, Wilma's travel time is  48 hours - 10 hours = 38 hours.


Let  d be the distance between the cities (the unknown value under the problem's question).


Then the time traveling from A to B is  {{{d/45}}}  hours;

     the time traveling back is  {{{d/50}}}  hours.


Total traveling time is 38 hours, giving this equation


    {{{d/45}}} + {{{d/50}}} = 38.    (1)


To solve it, multiply both sides by 450.  You will get


    10d + 9d = 38*450,

or

      19d     = 38*450,

        d     = {{{(38*450)/19}}} = 2*450 = 900.


<U>ANSWER</U>.  The distance between the cities A and B is 900 miles.


<U>CHECK</U>.   I will check the time equation (1):  {{{900/45}}} + {{{900/50}}} = 20 + 18 = 38  hours, total travel time.    ! Correct !
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Solved.