Question

Расстояние между пристанями А и В 115 целых 1/4км. В 9ч 30мин с пристани А по течению реки отплыл катер и одновременно с ним с пристани В против течения отплыл теплоход. Собственная скорость катера 18 целых 3/5км/ч, а собственная скорость теплохода 27 целых 1/2км/ч. Во сколько часов произойдёт встреча? Исследуйте, почему не дано значение скорости течения реки?

Answer 1

Для решения мы складываем скорости теплохода и катера 18,6 + 27,5 = 46,1 км/час - это общая скорость теплохода и катера, теперь расстояние между пристанями делим на общую скорость 115,25 : 46,1 = 2,5 часа. Значит время встречи 12 часов.

Answer 2

1) Возьмем за х км/ч - скорость течения реки, за y час - время прохождения пути , дроби переводим в десятичные - получаем уравнение:

((18,6 + х) + (27,5-х))*у=115,25

у=115,25/46,1

у=2,5

2) 2,5+9,5=12

В 12 часов дня произойдет встреча. А скорость течения реки не дана, т.к. при решении полжительное значение при сложении с отрицательным значением в результате дает ноль. 

 

Answer 3

Problem Analysis

We are given the following information: - The distance between two docks, A and B, is 115 1/4 km. - A boat departs from dock A and travels downstream with a speed of 18 3/5 km/h. - A ship departs from dock B and travels upstream with a speed of 27 1/2 km/h.

We need to determine the time at which the boat and ship will meet.

To solve this problem, we can use the formula: time = distance / relative speed. The relative speed is the difference between the speeds of the boat and ship.

However, we are not given the speed of the river current. This means we cannot directly calculate the relative speed. We will need to make some assumptions and perform calculations to find the answer.

Assumptions

To solve the problem, we will make the following assumptions: 1. The river current is constant throughout the journey. 2. The boat and ship travel in straight lines. 3. The boat and ship depart simultaneously.

Calculation

Let's calculate the time it takes for the boat and ship to meet.

1. We can represent the distance between the docks as the sum of the distances traveled by the boat and ship: - Let's assume the time taken for the boat and ship to meet is 't' hours. - The distance traveled by the boat in 't' hours is (18 3/5) * t km. - The distance traveled by the ship in 't' hours is (27 1/2) * t km. - The sum of these distances should be equal to the total distance between the docks: (18 3/5) * t + (27 1/2) * t = 115 1/4 km.

2. Now, we can solve the equation to find the value of 't': - (18 3/5) * t + (27 1/2) * t = 115 1/4 km. - Converting the mixed fractions to improper fractions: (93/5) * t + (55/2) * t = 461/4 km. - Finding a common denominator: (186/10) * t + (275/10) * t = 461/4 km. - Combining like terms: (461/10) * t = 461/4 km. - Dividing both sides by (461/10): t = (461/4) / (461/10). - Simplifying: t = (461/4) * (10/461). - Canceling out common factors: t = 10/4 = 2.5 hours.

Answer

Therefore, the boat and ship will meet after 2.5 hours.

Note: The problem does not provide the value of the river current. Without this information, we cannot calculate the exact speed of the river current or the exact time of the meeting. However, we can still determine the relative time at which the boat and ship will meet, assuming the river current is constant throughout the journey.