SOLUTION: A pleasure boat on the Mississippi River traveled from Baton Rouge to New Orleans with a stop at White Castle. On the first part of the trip, the boat traveled at an average speed

Algebra ->  Rational-functions -> SOLUTION: A pleasure boat on the Mississippi River traveled from Baton Rouge to New Orleans with a stop at White Castle. On the first part of the trip, the boat traveled at an average speed      Log On


   

Question 1200887: A pleasure boat on the Mississippi River traveled from Baton Rouge to New Orleans
with a stop at White Castle. On the first part of the trip, the boat traveled at an average speed of 10 mph. From White Castle to New Orleans the average speed was 15 mph. The entire trip covered 100 miles. How long did the entire trip take if the two parts each took the same number of hours?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.
A pleasure boat on the Mississippi River traveled from Baton Rouge to New Orleans
with a stop at White Castle. On the first part of the trip, the boat traveled
at an average speed of 10 mph. From White Castle to New Orleans the average speed
was 15 mph. The entire trip covered 100 miles. How long did the entire trip take
if the two parts each took the same number of hours?
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Let "d" be the unknown distance from Baton Rouge to White Castle.
Then the distance from White Castle to New Orleans is 100-d miles.


The travel time for the first part of the trip is  d%2F10  hours.

The travel time for the second part of the trip is  %28100-d%29%2F15  hours.


For these partial times we have this equation

    d%2F10  = %28100-d%29%2F15,

according to the problem.


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To solve the equation, multiply both sides by 150.  You will get

    15d = 10*(100-d).


Simplify and find "d"

    15d = 1000 - 10d

    15d + 10d = 1000

       25d    = 1000

         d    = 1000/25 = 40.


So, the distance from Baton Rouge to White Castle is 40 miles;
    the distance from White Castle to New Orleans is the rest 100-40 = 60 miles.


The total travel time is  40%2F10 + 60%2F15 = 4 + 4 = 8 hours.    ANSWER

Solved.

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It can be solved in different way/ways, too;

but this way will give you the maximum understanding.



Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The times for the two parts of the trip were the same, so the ratio of distances for the two parts is the same as the ratio of speeds.

The ratio of the speeds is 10:15 = 2:3, so 2/5 of the trip was at 10 mph and 3/5 was at 15 mph. Since the total trip was 100 miles, the first part of the trip was 40 miles and the second part was 60 miles.

The times for the two parts of the trip were 40/10 = 4 hours and 60/15 = 4 hours, so the total time for the trip was 8 hours.

ANSWER: 8 hours