Quadratic Equations

Question

A boat travelled 30km upstream, against the current, to deliver some feed from Elli, to Helmut's farm, it then turned around and headed 35km downstream to dock for the night. If the speed of the current was 3km/h and the upstream trip took 45min longer than the downstream trip, what was the speed of the boat?

Answer 1

If the speed of the boat was x km/h

Net speed upwards = (x-3).

Net speed downwards = (x+3)

Time upwards = 30 / (x-3)

Time downwards = 35 / (x+3)

Times in hours

45 minutes = 0.75 hrs

So 30/(x-3) = 35 / (x+3) + 0.75

Multiply through by (x-3)(x+3)

30 (x+3) = 35 (x-3) + 0.75 (x-3)(x+3)

30x + 90 = 35x - 105 + 0.75 (x²-9)

30x + 90 = 35x - 105 + 0.75x² - 6.75

0.75x² + 5 x -201.75 = 0

3x² + 20x -807√ = 0

Using quadratic formula x = (-20 +- √10084) / 6 = 13.4 km/h (taking the positive value of x)

Check.

Upstream. 30/10.4 = 2.88 hours

Downstream 35/16.4 = 2.13 hours

Difference 0.75 hours = 45 minutes