Question

The current of Cache Creek has speed 2 mph. It takes a small boat a total of 4 hours to travel 12 miles upstream and 12 miles back. Find the speed of the boat in still water. If your answer is not an integer, round it off to two decimal places.

Answer 1

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