Question

Два катера вышли одновременно навстречу друг другу из пунктов А и В, расстояние между которыми равно 150 км. через 1 ч 30 мин катера встретились и, не останавливаясь, продолжили путь с той же скоростью. Первый катер прибыл в В на 1 ч 15 мин позже, чем второй в А. сколько времени был в пути каждый катер??? помогите составить систему с двумя переменными)

Answer 1

На фотке решение!..........

Answer 2

Problem Analysis

We have two boats that start simultaneously from points A and B, which are 150 km apart. After 1 hour and 30 minutes, the boats meet and continue their journey at the same speed. The first boat arrives at point B 1 hour and 15 minutes later than the second boat arrives at point A. We need to find the time each boat spent on the journey.

Solution

Let's assume that the speed of each boat is v km/h. We can set up the following equations to solve the problem:

1. The time it takes for the boats to meet is 1 hour and 30 minutes, which is equal to 1.5 hours: - Distance covered by the first boat: 1.5v - Distance covered by the second boat: 1.5v

2. The time it takes for the first boat to reach point B is 1 hour and 15 minutes, which is equal to 1.25 hours: - Distance covered by the first boat: 1.25v + 150

3. The time it takes for the second boat to reach point A is the same as the time it takes for the boats to meet, which is 1.5 hours: - Distance covered by the second boat: 1.5v + 150

We can now solve these equations to find the value of v and then calculate the time each boat spent on the journey.

Calculation

Let's solve the equations:

1. Distance covered by the first boat = Distance covered by the second boat: - 1.5v = 1.5v

2. Distance covered by the first boat = Distance covered by the second boat: - 1.25v + 150 = 1.5v + 150

Simplifying the second equation: - 1.25v = 1.5v - 0.25v = 150 - v = 600

Now that we have the value of v, we can calculate the time each boat spent on the journey:

1. Time spent by the first boat: - Distance covered by the first boat = 1.25v + 150 - Time spent = (1.25v + 150) / v - Time spent = (1.25 * 600 + 150) / 600 - Time spent = 750 / 600 - Time spent = 1.25 hours or 1 hour and 15 minutes

2. Time spent by the second boat: - Distance covered by the second boat = 1.5v + 150 - Time spent = (1.5v + 150) / v - Time spent = (1.5 * 600 + 150) / 600 - Time spent = 900 / 600 - Time spent = 1.5 hours or 1 hour and 30 minutes

Answer

Each boat spent the following amount of time on the journey: - The first boat spent 1 hour and 15 minutes. - The second boat spent 1 hour and 30 minutes.

Please let me know if I can help you with anything else.