Question

Помогите,пожалуйста :( Группа туристов прошла 16 км.Первую часть пути туристы шли со скоростью 3.5 км/ч ,а вторую часть - со скоростью 3 км/ч.На вторую часть пути ушло на 1 час больше,чем на первую.Сколько времени затрачено на весь путь ? Сколько времени ушло на каждую часть пути ?

Answer 1

S1=v1*t1 - это первая часть пути
S2=v2*t2  - это вторая часть пути
S=S1+S2 - - это весь путь 16 км
v1=3,5 км/ч, v2=3 км/ч
т.к. на вторую часть пути ушло на 1 час больше времени, то
t2=t1+1. Значит,
S1=3.5*t1, S2=3*(t1+1)
Составляем уравнение:
3.5t1+3(t1+1)=16
3,5t1+3t1+3=16
6.5t1=13
t1=13/6.5
t1=2 (ч) - ушло времени на 1-ю часть пути
t2=2+1=3 (ч) - ушло времени на 2-ю часть пути
на весь путь затрачено 5 ч

Answer 2

Problem Analysis

We are given that a group of tourists traveled a total distance of 16 km. They traveled the first part of the distance at a speed of 3.5 km/h and the second part at a speed of 3 km/h. The second part of the journey took 1 hour longer than the first part. We need to find the total time taken for the entire journey and the time taken for each part of the journey.

Solution

Let's denote the time taken for the first part of the journey as t1 and the time taken for the second part as t2.

We can use the formula distance = speed × time to set up two equations based on the given information:

Equation 1: 3.5t1 = distance of the first part

Equation 2: 3t2 = distance of the second part

We also know that t2 = t1 + 1 (the second part took 1 hour longer than the first part).

To solve this system of equations, we can substitute the value of t2 from Equation 3 into Equation 2:

3(t1 + 1) = distance of the second part

Simplifying this equation, we get:

3t1 + 3 = distance of the second part

Now we have two equations with two unknowns. We can solve them simultaneously to find the values of t1 and t2.

Let's substitute the values of the distances into the equations:

Equation 1: 3.5t1 = 16

Equation 2: 3t2 = 16

Solving Equation 1 for t1, we get:

t1 = 16 / 3.5

Solving Equation 2 for t2, we get:

t2 = 16 / 3

Now we can calculate the values of t1 and t2.

Calculation

Using the given values, we can calculate the time taken for each part of the journey:

t1 = 16 / 3.5 = 4.57 hours

t2 = 16 / 3 = 5.33 hours

To find the total time taken for the entire journey, we add t1 and t2:

Total time = t1 + t2 = 4.57 + 5.33 = 9.9 hours

Answer

The total time taken for the entire journey is 9.9 hours. The time taken for the first part of the journey is approximately 4.57 hours, and the time taken for the second part of the journey is approximately 5.33 hours.

Please note that the calculated values are approximate due to rounding.

Let me know if there's anything else I can help you with!