Question

Расстояние между двумя пунктами по реке равно 80км . Это расстояние лодка проплывает по течению за 4 часа, а против течения за 5 часов . Найдите собственную скорость лодки и скорость течение реки .

Answer 1

Пусть х - скорость лодкиу - скорость рекитогда (х+у)4=80, (х-у)5=80поясняю, что х+у - это скорость лодки по течениюх-у  - против течениятогда х-у = 16, то есть х = у+16подставляем в первое уравнениеу+16+у = 80/42у = 4у = 2подставляем х = 18+2= 20

Answer 2

Problem Analysis

We are given that the distance between two points on a river is 80 km. The boat takes 4 hours to travel this distance downstream and 5 hours to travel the same distance upstream. We need to find the speed of the boat and the speed of the river's current.

Solution

Let's assume the speed of the boat is v km/h and the speed of the river's current is c km/h.

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the current. Therefore, the boat's effective speed downstream is v + c km/h.

Similarly, when the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the current. Therefore, the boat's effective speed upstream is v - c km/h.

We can use the formula distance = speed × time to set up two equations based on the given information:

1. When the boat is traveling downstream: - Distance = 80 km - Speed = v + c km/h - Time = 4 hours

2. When the boat is traveling upstream: - Distance = 80 km - Speed = v - c km/h - Time = 5 hours

We can solve these equations to find the values of v and c.

Calculation

Let's solve the equations:

1. When the boat is traveling downstream: - Distance = Speed × Time - 80 = (v + c) × 4 - 80 = 4v + 4c 2. When the boat is traveling upstream: - Distance =