Question

Из поселка А в поселок В вышел турист со скоростью 6,8 км/ч, а из поселка В в поселок А вышел второй турист со скоростью 6,5 км/ч. На расстоянии 17 км от посёлка А туристы встретились. На сколько часов раньше вышел первый турист, если расстояние между поселками 27,4 км? *И напишите пояснение пожалуйста. Заранее спасибо)))

Answer 1

1)17:6.8=2.5 (ч.) - прошёл 1 турист (17 км)
2)27.4-17=10.4 (км) - прошёл 2 турист
3)10.4:6.5=1.6 (ч.) - прошёл 2 турист (10.4 км)
4)2.5-1.6=0.9 (ч.) 
Ответ: на 0.9 часов 1 турист вышел раньше 2 туриста.

Answer 2

Problem Analysis

To solve this problem, we need to determine how much earlier the first tourist left compared to the second tourist, given their speeds and the distance between the two villages.

Solution

Let's denote: - \( t_1 \) as the time taken by the first tourist to reach the meeting point. - \( t_2 \) as the time taken by the second tourist to reach the meeting point. - \( d \) as the distance between the two villages. - \( v_1 \) as the speed of the first tourist. - \( v_2 \) as the speed of the second tourist.

We can use the formula: \[ \text{time} = \frac{\text{distance}}{\text{speed}} \]

The time taken by the first tourist to reach the meeting point is given by: \[ t_1 = \frac{d}{v_1} \]

The time taken by the second tourist to reach the meeting point is given by: \[ t_2 = \frac{d}{v_2} \]

The difference in their times is: \[ \Delta t = t_2 - t_1 \]

Calculation

Given: - \( d = 27.4 \, \text{km} \) - \( v_1 = 6.8 \, \text{km/h} \) - \( v_2 = 6.5 \, \text{km/h} \)

Using the above formulas, we can calculate: \[ t_1 = \frac{27.4}{6.8} \] \[ t_2 = \frac{27.4}{6.5} \] \[ \Delta t = t_2 - t_1 \]

Result

The first tourist left \( \Delta t \) hours earlier than the second tourist.

Calculation Result

\[ t_1 \approx 4.029 \, \text{hours} \] \[ t_2 \approx 4.215 \, \text{hours} \] \[ \Delta t \approx 0.186 \, \text{hours} \]

So, the first tourist left approximately 0.186 hours earlier than the second tourist.

Explanation

The first tourist left earlier than the second tourist because they were traveling at a slightly faster speed. This allowed the first tourist to cover the distance in less time, resulting in the meeting occurring earlier than if both tourists were traveling at the same speed.

This explanation is based on the formula for calculating time using distance and speed, and it aligns with the principles of relative motion and speed.

I hope this helps! If you have further questions, feel free to ask!