SOLUTION: 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

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 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      Log On


   

Question 1185319: 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?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
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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%2F45  hours;

     the time traveling back is  d%2F50  hours.


Total traveling time is 38 hours, giving this equation


    d%2F45 + d%2F50 = 38.    (1)


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


    10d + 9d = 38*450,

or

      19d     = 38*450,

        d     = %2838%2A450%29%2F19 = 2*450 = 900.


ANSWER.  The distance between the cities A and B is 900 miles.


CHECK.   I will check the time equation (1):  900%2F45 + 900%2F50 = 20 + 18 = 38  hours, total travel time.    ! Correct !

Solved.



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


First a standard algebraic setup for solving the problem....

d = distance between A and B

time going from A to B: d/45
time going from B to A: d/50

Total driving time: 48-10=38

d%2F45%2Bd%2F50=38

Solve using basic algebra; probably start by multiplying both sides by a common denominator to clear fractions.

I leave it to you to finish solving the problem by that method.

Here is a very different way of solving the problem....

The distances both directions are the same; the ratio of speeds is 50:45=10:9. That means the ratio of times spent at the two speeds is 9:10.

So let the time at 50mph be 9x and the time at 45mph be 10x.

The total time is 38 hours:

9x%2B10x=38
19x=38
x=2

The time at 50mph is 9x=18 hours; that means the distance between A and B is 50(18)=900 miles.

Note also the time at 45mph is 10x=20 hours, which means the distance between A and B is 45(20)=900 miles -- which of course agrees with the answer we already found.