Final answer:
To calculate the speed of the boat in still water, we create equations for the upriver and downriver trips considering the current's speed, sum the time for both trips, and solve for the speed variable 'b'.
Step-by-step explanation:
The question asks to determine the speed of the boat in still water when given Kerrie's upriver and downriver times, along with the current's speed. In this problem, the boat's speed in still water is a variable we can call 'b', and the speed of the current is given as 5 mph. The total trip is 15 miles upriver and 15 miles back, taking 4 hours.
To solve the problem, we need to set up two equations representing the upriver and downriver trips. With 'b' as the boat's speed in still water:
- Going upriver at speed (b - 5), because the current is against her, the time taken to travel 15 miles is 15 / (b - 5).
- Coming back downriver at speed (b + 5), because the current helps her, the time taken is 15 / (b + 5).
The total time for both trips must add up to 4 hours:
15 / (b - 5) + 15 / (b + 5) = 4
This equation can be solved to find the value of 'b', the speed of the boat in still water. Solving the equation:
(multiply both sides by (b - 5)(b + 5) to clear the denominators)
15(b + 5) + 15(b - 5) = 4(b - 5)(b + 5)
Simplify and solve the quadratic equation to find the value of 'b'.