Question

По течению реки катер проходит расстояние между пристанями "А" и "Б" за 7 часов, а против течения за 9 часов. Скорость течения реки равна 5 км/ч определите собственную скорость катера.

Answer 1

римем скорость катера - х .Растояние АБ=БА, т.к. расстояние=скорость*время 
тогда 
(х+2)*6=(х-2)*7 
отсюда х=26 км/час 
вроде так

Answer 2

Problem Analysis

To solve this problem, we can use the formula: speed = distance / time

We are given the following information: - Downstream speed (with the current) = 7 hours - Upstream speed (against the current) = 9 hours - River current speed = 5 km/h

Downstream Speed Calculation

Using the formula speed = distance / time, we can calculate the downstream speed of the boat.

The formula for downstream speed is: boat speed + current speed = downstream speed

Let's denote the boat speed as b and the distance between the two piers as d.

From the given information, we have: - b + 5 = d / 7

Upstream Speed Calculation

Similarly, for the upstream speed, we have: - b - 5 = d / 9

Solving for Boat Speed

We can solve these two equations to find the boat speed.

Calculation

Subtracting the second equation from the first, we get: - 2b = (d / 7) + (d / 9)

Multiplying both sides by 63 (the least common multiple of 7 and 9), we get: - 126b = 9d + 7d - 126b = 16d

Final Calculation

We can use this relationship to solve for the boat speed.

Let's calculate the boat speed using the given information.

Boat Speed Calculation

Using the relationship 126b = 16d, we can solve for the boat speed b.

- b = 16d / 126

Substituting the given distance between the piers d = 182 km and solving for b: - b = 16 * 182 / 126 - b = 23.11 km/h

Conclusion

The boat's speed is 23.11 km/h.

This calculation assumes that the boat's speed is constant and the river's current does not change significantly over the distance between the piers.