Question

Помогите решить: машина сначала проехала 455км,а затем еще 260км с постоянной скоростью. сколько часов машина была в пути, если вторую часть пути она проехала на 3 часа быстрее,чем первую?

Answer 1

(455-260)/3=65км/ч
(455+260)/65=11ч

Answer 2

Problem Analysis

To solve this problem, we need to find the total time the car was on the road. We know that the car first traveled 455 km and then an additional 260 km at a faster speed. The second part of the journey took 3 hours less than the first part. We need to determine the total time the car was on the road.

Solution

Let's assume that the car's speed during the first part of the journey was x km/h. Since the car traveled 455 km during this part, we can calculate the time it took using the formula:

Time = Distance / Speed

So, the time taken for the first part of the journey is:

Time1 = 455 km / x km/h

During the second part of the journey, the car traveled 260 km at a faster speed. Let's assume the speed during this part was y km/h. We know that the second part of the journey took 3 hours less than the first part. Therefore, the time taken for the second part of the journey is:

Time2 = (455 km + 260 km) / y km/h = 715 km / y km/h

We also know that the second part of the journey took 3 hours less than the first part. So, we can write the equation:

Time1 - Time2 = 3 hours

Substituting the values of Time1 and Time2, we get:

(455 km / x km/h) - (715 km / y km/h) = 3 hours

To solve this equation, we need to eliminate the variables x and y. We can do this by multiplying both sides of the equation by xy:

455y - 715x = 3xy

Now, we need to find a relationship between x and y. From the given information, we know that the second part of the journey was completed in 3 hours less time than the first part. So, we can write:

Time2 = Time1 - 3 hours

Substituting the values of Time1 and Time2, we get:

(715 km / y km/h) = (455 km / x km/h) - 3 hours

To eliminate the variables x and y, we can multiply both sides of the equation by xy:

715x = 455y - 3xy

Now, we have a system of equations:

455y - 715x = 3xy 715x = 455y - 3xy

We can solve this system of equations to find the values of x and y. Once we have the values of x and y, we can calculate the total time the car was on the road by adding Time1 and Time2.

Let's solve the system of equations to find the values of x and y.