Question

Велосипедист должен был проехать весь путь с определенной скоростью за 2 часа. Но он ехал со скоростью, превышающей намеченную на 3 км/ч, поэтому на весь путь затратил 1,3 часа. Найдите длину пути.

Answer 1

Пусть скорость велосипедиста х км/ч, за 2 часа велосипедист должен был проехать 2х км.
Так как велосипедист ехал со скоростью (х+3) км/ч и затратил на путь 1,3 часа, то
2х=1,3·(х+3)
2х=1,3х+3,9
0,7х=3,9
х=39/7

Путь  2х=2·39/7=78/7=11 целых 1/7 км

Answer 2

Problem Analysis

A cyclist was supposed to complete a certain distance in 2 hours at a specific speed. However, the cyclist ended up traveling at a speed 3 km/h faster than planned and took 1.3 hours to complete the entire distance. We need to find the length of the path.

Solution

Let's assume the planned speed of the cyclist was x km/h. Since the cyclist traveled 3 km/h faster than planned, the actual speed was x + 3 km/h.

We know that time is equal to distance divided by speed. Using this formula, we can set up the following equations:

1. Planned time: 2 hours = Distance / Planned Speed 2. Actual time: 1.3 hours = Distance / Actual Speed

To find the length of the path, we need to solve these equations simultaneously.

Calculating the Length of the Path

Let's solve the equations:

1. Planned time: 2 hours = Distance / Planned Speed - Distance = 2 * Planned Speed

2. Actual time: 1.3 hours = Distance / Actual Speed - Distance = 1.3 * Actual Speed

Since both equations represent the same distance, we can equate them:

2 * Planned Speed = 1.3 * Actual Speed

Simplifying the equation:

2 * (x) = 1.3 * (x + 3)

Now, we can solve for x, which represents the planned speed:

2x = 1.3x + 3.9 0.7x = 3.9 x = 3.9 / 0.7 x ≈ 5.5714

The planned speed was approximately 5.5714 km/h.

To find the length of the path, we can substitute the planned speed into the equation for distance:

Distance = 2 * Planned Speed Distance ≈ 2 * 5.5714 Distance ≈ 11.1428 km

Therefore, the length of the path is approximately 11.1428 km.

Answer

The length of the path is approximately 11.1428 km.