Question

Катер проплыл 33 км вниз по течению реки, а затем такое же время плыл против течения, пройдя при этом 27 км. В стоячей воде катер плывёт со скоростью 20км/ч. Сколько времени длилось путешествие

Answer 1

Пусть х - скорость течения реки, тогда

33/(20+х)=27/(20-х)

Получается пропорция, умножаем крест/накрест
33(20-x)=27(20+x)

Раскрываем скобки и приводим подобные слагаемые
660-33х=540+27х
60х=120
х=2

Подставляем найденное значение в уравнение

33/(20+2)=27/(20-2)

33/22+27/18=3

Значит, путешествие длилось 3ч

Answer 2

Calculation of Travel Time

To calculate the total travel time, we need to consider the time taken to travel downstream and the time taken to travel upstream.

Let's denote the speed of the boat in still water as v (20 km/h), the speed of the current as c, the time taken to travel downstream as t1, and the time taken to travel upstream as t2.

Given that the boat traveled 33 km downstream and 27 km upstream, we can set up the following equations:

1. Downstream: (v + c) × t1 = 33 km 2. Upstream: (v - c) × t2 = 27 km

To find the values of t1 and t2, we need to solve these equations.

Solving the Equations

Let's solve the equations using the given information.

From equation 1, we have (v + c) × t1 = 33 km. Rearranging the equation, we get:

t1 = 33 km / (v + c)

From equation 2, we have (v - c) × t2 = 27 km. Rearranging the equation, we get:

t2 = 27 km / (v - c)

Now, let's substitute the value of v (20 km/h) into the equations:

t1 = 33 km / (20 km/h + c)

t2 = 27 km / (20 km/h - c)

To find the total travel time, we need to add the time taken to travel downstream and the time taken to travel upstream:

Total travel time = t1 + t2

Let's calculate the total travel time using the given information.

Calculation

Substituting the values into the equations:

t1 = 33 km / (20 km/h + c)

t2 = 27 km / (20 km/h - c)

To find the total travel time, we add t1 and t2:

Total travel time = t1 + t2

Now, we need to find the value of c (the speed of the current) to calculate the total travel time. Unfortunately, the given information does not provide the value of c. Without this information, we cannot calculate the exact total travel time.

Please provide the value of c (the speed of the current) so that we can calculate the total travel time accurately.