The boat passed against the current for 247 km and returned to the pier, spending 6 hours

The boat passed against the current for 247 km and returned to the pier, spending 6 hours less on the way back. Find the current speed if the boat speed is 16 km / h.

We denote the speed of the current by y km / h and compose an equation where the speed of the boat downstream is equal to (y + 16) km / h, and upstream is equal to (16 – y) km / h:

247 / (16 – y) = 247 / (y + 16) + 6;

247 * (16 + y) = 247 * (16 – y) + 6 * (16 – y) * (16 + y);

247 * 16 + 247 * y = 247 * 16 – 247 * y + 6 * (256 – y ^ 2);

247 * y = -247 * y + 6 * 256 – 6 * y ^ 2;

6 * y ^ 2 + 494 * y – 1536 = 0; (we solve the quadratic equation);

D = 244036 + 36864 = 280900;

y1 = (-494 + 530) / 12 = 3;

y2 = (-494 – 530) / 12 = -85.3; (speed cannot be negative);

Answer: the current speed is 3 km / h.