Question 701751: For the following problem, clearly define the variable(s) and write an equation that could be used to solve the problem. What are the units of the answer.
Two tugboats that have the same speed in still water travel in opposite directions in a river with a constant current of 5 miles per hour. The tugboats departed at the same time from a refueling station; and after a period of time, one has traveled 30 miles downstream and the other has traveled 6 miles upstream. Determine the rate of each boat in still water.
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! The tugboat going upstream is slowed by 5 mph, so speed is r-5 mph; letting r equal speed in still water. The tugboat going downstream is going WITH the current and its speed is increased by 5 mph, so speed is r+5 mph.
Let t = time in hours.
One can make a table using this format:
Which Direction: Speed(miles per hour), Time(hours), Distance(miles)
Upstream: r-5, t, 30
Downstream: r+5, t, 6
Find two expressions for the travel time, which are equal for the both boats.
Upstream, 
Downstream, 
The formulas for t are equal, so
Most of the effort is analyzing the situation and setting up the relationship equation. Solve for r.
Answer by josmiceli(19441)  (Show Source):
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