SOLUTION: The barges traveled downstream at 12 mph and upstream at 7 mph. What was their downstream travel time if it was 10 hours less than the time required to travel the same distance ups

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Question 1206933: The barges traveled downstream at 12 mph and upstream at 7 mph. What was their downstream travel time if it was 10 hours less than the time required to travel the same distance upstream?
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52905) About Me  (Show Source):
You can put this solution on YOUR website!
.
The barges traveled downstream at 12 mph and upstream at 7 mph.
What was their downstream travel time if it was 10 hours less
than the time required to travel the same distance upstream?
~~~~~~~~~~~~~~~~~~~ 

It is easy.


Let t be the downstream travel time, in hours.

Then the upstream travel time is (t+10) hours, according to the problem.


The travel distance downstream is 12t      miles (the rate times time);
The travel distance   upstream is  7(t+10) miles (the rate times time).


So, we write this equation

    12t = 7*(t+10)

saying that the travel distance is the same in both directions.


Simplify and find t

    12t = 7t + 70

    12t - 7t = 70

        5t   = 70

         t   = 70/5 = 14.


ANSWER.  The downstream travel time is 14 hours.

Solved.



Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
                 SPEED         TIME           DISTANCE
DOWNSTR           12           x-10              d
UPSTRM             7            x                d

Same distance d each direction. SPEED*TIME=DISTANCE.

12%28x-10%29=7x
-
12x-120=7x
5x=120
x=24-------upstream travel time

DOWNSTREAM time was x-10=24-10=highlight%2814%2Ahours%29.

Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a different way to start on solving the problem that leads quickly to the same equation shown in the solutions by the other tutors.

Let x be the downstream travel time; then x+10 is the upstream travel time.

The ratio of the speeds is 7:12; since the distances are the same, the times are in the same ratio:

7%2F12=x%2F%28x%2B10%29
12x=7%28x%2B10%29
12x=7x%2B70
5x=70
x=14

ANSWER: 14 hours

CHECK:
downstream x=14 hours at 12mph = 14*12 = 168 miles
upstream x+10=24 hours at 7mph = 24*7 = 168 miles