The motor boat passed 32 km along the river and returned back, spending 6 hours for the entire journey

| January 29, 2021 | education

The motor boat passed 32 km along the river and returned back, spending 6 hours for the entire journey. Find the speed of the boat in still water if the current speed is 4 km / h.

1. Let X km / h be the speed of a motor boat without a current.

So (X + 4) km / h is its speed downstream, (X – 4) km / h – against.

2. The way of a motor boat in one direction is 32 km.

Then the travel time downstream is 32 / (X + 4) hours, and against 32 / (X – 4) km / h.

The whole journey took 6 hours.

3. We get the equation.

32 / (X – 4) + 32 / (X + 4) = 6.

32 * X + 32 * 4 + 32 * X – 32 * 4 = 6 * X * X – 6 * 16.

3 * X * X – 32 * X – 48 = 0.

Discriminant D = 32 * 32 + 12 * 48 = 1024 + 576 = 1600.

X = (32 + 40) / 6 = 72/6 = 12 km / h.

Answer: The speed of the motor boat is 12 km / h.



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