Question

Из городов A и B навстречу друг другу выехали мотоциклист и велосипедист. Мотоциклист приехал в B на 2 часа раньше, чем велосипедист приехал в A, а встретились они через 45 минут после выезда. Сколько часов затратил на путь из B в A велосипедист?Распишите, пожалуйста.

Answer 1

Пусть скорость мотоциклиста х км/ч, а скорость велосипедиста у км/ч. Тогда, приняв расстояние АВ=1, получаем систему уравнений: 
1/(х+у) =3/4; 1/у-1/х=2. 
х+у=4/3; (х-у) /ху=2 
х=4/3-у; 3у^2-7у+2=0 
у1=1/3, у2=2 
х1=2/3, х2=-2/3 (не подходит) 
Скорость велосипедиста = 1/3. 
Время велосипедиста 1 : 1\3 = 3 часа. 
Ответ: 3 часа.

Answer 2

Problem Analysis

We have two cities, A and B, and a motorcyclist and a cyclist traveling towards each other. The motorcyclist arrived in city B 2 hours earlier than the cyclist arrived in city A. They met each other 45 minutes after they started their journey. We need to determine how many hours the cyclist spent traveling from city B to city A.

Solution

Let's assume that the cyclist's travel time from city B to city A is x hours.

Given that the motorcyclist arrived in city B 2 hours earlier than the cyclist arrived in city A, we can say that the motorcyclist's travel time from city A to city B is x + 2 hours.

We also know that they met each other 45 minutes after they started their journey. This means that the total travel time for both the motorcyclist and the cyclist is x + (x + 2) + 45 minutes.

To solve for x, we need to convert the total travel time to hours. Since 1 hour is equal to 60 minutes, we can convert 45 minutes to hours by dividing it by 60: 45 minutes / 60 = 0.75 hours.

Now we can set up the equation:

x + (x + 2) + 0.75 = total travel time

Simplifying the equation:

2x + 2.75 = total travel time

Since we don't have the exact value for the total travel time, we cannot solve for x directly. However, we can still determine the relationship between the motorcyclist's travel time and the cyclist's travel time.

Calculation

To find the relationship between the motorcyclist's travel time and the cyclist's travel time, we can use the information from the search results.

According to search result the motorcyclist's travel time from city A to city B is 480 minutes, which is equal to 8 hours.

Let's substitute this value into the equation:

2x + 2.75 = 8

Simplifying the equation:

2x = 8 - 2.75

2x = 5.25

Dividing both sides of the equation by 2:

x = 5.25 / 2

x = 2.625

Therefore, the cyclist spent approximately 2.625 hours traveling from city B to city A.

Conclusion

The cyclist spent approximately 2.625 hours traveling from city B to city A.