Question

Моторная лодка проплыла по течению реки от пристани А до пристани В за 20 часов, а от пристани В до пристани А за 30 часов. За какое время моторная лодка проплывет путь , равный АВ , двигаясь по озеру?

Answer 1

{
Пояснение
s - расстояние от A до B
v - скорость моторной лодки
d - скорость течения реки
}

s / (v + d) = 20 {при движении по течению реки, собственная скорость лодки складывается со скоростью течения реки, т.е. v + d}
s / (v - d) = 30 {при движении против течения - скорость течения наоборот вычитается из скорости лодки}
s / v = ? {здесь, при движении по озеру, на скорость лодки ничего не влияет}

v + d = s/20
v - d = s/30 {эти две строки получены из первых двух}

2v = s/20 + s/30 = 5s/60 = s/12 {эту строку можно получить, сложив две предыдущие}
v = s/24

s / v = s / (s / 24) = 24

Answer 2

Problem Analysis

We are given that a motorboat traveled from pier A to pier B in 20 hours, and from pier B to pier A in 30 hours. We need to determine how long it will take for the motorboat to travel the distance AB while moving on a lake.

Solution

To solve this problem, we need to consider the relative speeds of the motorboat and the river current. Let's assume that the speed of the motorboat in still water is M and the speed of the river current is C.

When the motorboat is traveling from pier A to pier B, it is moving against the current. Therefore, the effective speed of the motorboat is M - C. We can use the formula distance = speed × time to calculate the distance AB:

AB = (M - C) × 20 Similarly, when the motorboat is traveling from pier B to pier A, it is moving with the current. Therefore, the effective speed of the motorboat is M + C. We can use the same formula to calculate the distance BA:

BA = (M + C) × 30 Since AB and BA represent the same distance, we can equate them:

(M - C) × 20 = (M + C) × 30

Now, we can solve this equation to find the values of M and C. Once we have those values, we can calculate the time it will take for the motorboat to travel the distance AB on the lake.

Let's solve the equation:

20M - 20C = 30M + 30C

10M = 50C

M = 5C

Now, we can substitute the value of M in terms of C into one of the equations to find the value of C:

AB = (5C - C) × 20

AB = 4C × 20

AB = 80C

Since AB represents the distance on the lake, we can use the formula distance = speed × time again to calculate the time it will take for the motorboat to travel the distance AB on the lake:

AB = 80C × time

time = AB / (80C)

Therefore, the motorboat will take AB / (80C) hours to travel the distance AB on the lake.

Answer

The motorboat will take AB / (80C) hours to travel the distance AB on the lake, where AB is the distance between pier A and pier B, and C is the speed of the river current.

Please note that we need the specific values of AB and C to calculate the exact time.