SOLUTION: Please help me solve this equation: In going over a round trip of 40 km each way, it takes a course travelling 12 kph in still water, having a total time of 7 hours and a half. W

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Question 831391: Please help me solve this equation:
In going over a round trip of 40 km each way, it takes a course travelling 12 kph in still water, having a total time of 7 hours and a half. What was the rate of the river current?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Your boat travels at 12 kilometers per hour in still water.
In a river with a current flowing at a speed of x kilometers per hour,
the boat will advance (as seen from the shore) at %2812-x%29 kph when going upstream, against the current.
When going downstream, the boat will move at %2812%2Bx%29 kph relative to the shore.
The 40 kilometer trip upstream will take
40%2F%2812-x%29 hours.
The 40 kilometer trip downstream will take
40%2F%2812%2Bx%29 hours.
Adding those times we would get the total time of 7.5 hours, so our equation is
40%2F%2812-x%29%2B40%2F%2812%2Bx%29=7.5

Solving:
40%2F%2812-x%29%2B40%2F%2812%2Bx%29=7.5

%28480%2B40x%29%2F%28144-x%5E2%29%2B%28480-40x%29%2F%28144-x%5E2%29=7.5
%28480%2B40x%2B480-40x%29%2F%28144-x%5E2%29=7.5
960%2F%28144-x%5E2%29=7.5
960=7.5%28144-x%5E2%29
960=1080-7.5x%5E2
7.5x%5E2=1080-960
7.5x%5E2=120
x%5E2=120%2F7.5
x%5E2=16
Since we measured the rate of the current in the direction of the flow as a positive number,
highlight%28x=sqrt%2816%29=4%29 .
The rate of the current is highlight%284kph%29 .