Answer:
6 = 5/(x+2) +5/(x -2)
Step-by-step explanation:
You want a rational equation that expresses a total travel time of 6 hours for a trip downstream 5 miles and back in a raft of speed x with respect to a current of speed 2 miles per hour.
Speed
The speed of travel downstream is the sum of the raft speed and the current speed: x +2.
The speed of travel upstream is the difference of raft speed and the current speed: x -2.
Time
The travel time is the distance divided by the speed of travel. We want the total travel time to be 6 hours, so we will add the downstream time and the upstream time:
6 = 5/(x+2) +5/(x -2) . . . . . . your rational equation
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Additional comment
The solution of interest is x = 3 miles per hour. This makes the raft take 1 hour to go downstream and 5 hours to return. You may also see an extraneous solution of x = -4/3.
