The current in a stream moves at a speed of 4 mph. A boat travels 24 mi upstream and 24 mi downstream in a total time of 14 hrs. What is the speed of the boat in still water?
since time = distance/speed,
24/(x-4) + 24/(x+4) = 14
To find the speed of the boat in still water, we need to understand the concept of relative velocity.
Let's assume the speed of the boat in still water is "b" mph, and the speed of the current is "c" mph.
When the boat is traveling upstream, it moves against the current, so its effective speed is reduced by the speed of the current. Therefore, the boat's speed upstream is (b - c) mph.
Conversely, when the boat is traveling downstream, it moves with the current, so its effective speed is increased by the speed of the current. Therefore, the boat's speed downstream is (b + c) mph.
According to the problem, the boat travels 24 miles upstream and 24 miles downstream. The total time taken for these two trips is 14 hours.
Let's set up the equation:
Time taken for upstream trip + Time taken for downstream trip = Total time
Distance รท Speed = Time
(24 miles / (b - c) mph) + (24 miles / (b + c) mph) = 14 hours
Now, we need to solve this equation to find the value of "b" (the speed of the boat in still water).