Question

Расстояние между двумя пристанями по течению реки катер прошел за 7 часов, а против течения за 8 часов. Найдите скорость течения реки, если собственная скорость катера равна 21 км/ч?

Answer 1

Таблица:
                                  S              U                  T
1)По течению          (21+x)*7       21+x            7
2)Против течения    (21-x)*8        21-x             8
Уравнение:
(21+x)*7=(21-x)*8 
7x+147= - 8x + 168
15x = 21
x=21/15
x=1,4                               Ответ:U=1,4 

Answer 2

Problem Analysis

We are given that a boat traveled between two ports along a river. It took 7 hours to travel downstream (with the current) and 8 hours to travel upstream (against the current). We need to find the speed of the river's current, given that the boat's own speed is 21 km/h.

Downstream Speed Calculation

To calculate the downstream speed, we can use the formula: downstream speed = boat's speed + current's speed.

Let's denote the downstream speed as d and the speed of the current as c. We know that the boat's speed is 21 km/h. Therefore, the downstream speed can be calculated as follows:

d = 21 + c

Upstream Speed Calculation

To calculate the upstream speed, we can use the formula: upstream speed = boat's speed - current's speed.

Let's denote the upstream speed as u. Using the same boat speed of 21 km/h, the upstream speed can be calculated as follows:

u = 21 - c

Distance Calculation

We are also given the time it took for the boat to travel between the two ports in each direction. The distance traveled can be calculated using the formula: distance = speed × time.

Let's denote the distance traveled downstream as D and the distance traveled upstream as U. We know that the time taken downstream is 7 hours and the time taken upstream is 8 hours. Therefore, the distances can be calculated as follows:

D = d × 7 U = u × 8

Relationship between Distance, Speed, and Time

Since the distance traveled downstream is the same as the distance traveled upstream, we can equate the two distances:

D = U

Substituting the previously calculated values for D and U:

d × 7 = u × 8

Solving for the Current's Speed

Now we can solve the equation to find the speed of the current:

21 + c × 7 = 21 - c × 8

Simplifying the equation:

7c + 8c = 21 - 21

15c = 0

c = 0

The speed of the river's current is 0 km/h.

Answer

The speed of the river's current is 0 km/h.

Conclusion

The boat's speed of 21 km/h is equal to the speed of the current. Therefore, the boat is traveling at the same speed as the current, resulting in a net speed of 0 km/h when traveling upstream or downstream.