Answer:
6.61 mph
Step-by-step explanation:
Speed of current; c = 2 mph
Total time to travel upstream and back; t = t1 + t2 = 4 hours
Let x represent speed of the boat in still water
Then the actual speed of the boat when going
upstream is x - 2, and the actual speed when going downstream downstream is x + 2.
We know that; distance = speed x time, Thus;
For the upstream trip;
12 = (x - 2)t1
t1 = 12/(x - 2)
For the downstream trip;
12 = (x + 2)t2
t2 = 12/(x +2)
Adding both equations, we have;
t1 + t2 = (12/(x - 2)) + (12/(x +2))
4 = (12/(x - 2)) + (12/(x +2))
Multiply through by (x - 2)(x + 2)
4(x - 2)(x + 2) = 12(x + 2) + 12(x - 2)
4x²- 16 = 12x + 24 + 12x - 24
4x² - 16 = 24x
4x² - 24x - 16 = 0
Using quadratic formula, we have;
x ≈ 6.61 mph
