Question

При движении против течения реки расстояние 126 км моторная лодка проходит за 7ч. Какова скорость лодки в стоячей воде, если плот то же расстояние проходит за 63ч?

Answer 1

126:7=18км/ч скорость лодки против течения
126:63=2км/ч скорость течения
18-2=16км/ч скорость лодки в стоячей воде

Answer 2

Calculation of Boat Speed in Still Water

To calculate the speed of the boat in still water, we can use the concept of relative velocity. The boat's speed in still water can be determined by subtracting the speed of the river's current from the boat's speed when moving against the current.

Let's denote the speed of the boat in still water as v and the speed of the river's current as c.

Given that the boat covers a distance of 126 km in 7 hours when moving against the current, we can set up the following equation:

126 km = (v - c) × 7 hours Similarly, when the boat is moving with the current, it covers the same distance of 126 km in 63 hours. We can set up another equation:

126 km = (v + c) × 63 hours To find the speed of the boat in still water, we need to solve these two equations simultaneously.

Solving the Equations

Let's solve the equations using the method of substitution.

From the first equation, we can express v in terms of c:

v = (126 km / 7 hours) + c

Substituting this value of v into the second equation, we get:

(126 km) = [(126 km / 7 hours) + c + c] × 63 hours

Simplifying the equation:

126 = (18 + 2c) × 63

126 = 1134 + 126c

Rearranging the equation:

126c = -1008

c = -8 km/h

Now, substituting the value of c back into the equation for v, we get:

v = (126 km / 7 hours) - 8 km/h

Simplifying:

v = 18 - 8

v = 10 km/h

Answer

Therefore, the speed of the boat in still water is 10 km/h