Question

Из двух пунктов, расстояние между которыми 222,6 км, одновременно навстречу друг другу выехали два поезда. Они встретились через 5,3 ч. Какое расстояние проехал первый поезд, если скорость первого поезда составляет 20% скорости второго? ДАЮ 20Б

Answer 1

1) 222,6 км : 5,3 ч = 42 км/ч - скорость сближения
2) Примем скорость 2-го поезда за 1 часть , тогда
скорость 1-го поезда 0,2 части ( т к 20%=0,2)
1+0,2=1,2 части приходится на скорость сближения
3) 42км/ч :1,2= 35 км/ч скорость 2-го поезда
4) 42-35=7 км/ч - скорость 1- го поезда
5) 7 км/ч * 5,3 ч=37,1 км - проехал 1-й поезд

Answer 2

Problem Analysis

We are given that two trains start simultaneously from two points that are 222.6 km apart and travel towards each other. They meet after 5.3 hours. We need to find the distance traveled by the first train, given that its speed is 20% of the speed of the second train.

Solution

Let's assume the speed of the second train is x km/h. Then the speed of the first train is 0.2x km/h, as it is 20% of the speed of the second train.

We can use the formula distance = speed × time to find the distance traveled by each train.

The first train travels for 5.3 hours at a speed of 0.2x km/h, so the distance traveled by the first train is (0.2x) × 5.3 km.

The second train also travels for 5.3 hours at a speed of x km/h, so the distance traveled by the second train is x × 5.3 km.

Since the total distance between the two trains is 222.6 km, we can write the equation:

(0.2x) × 5.3 + x × 5.3 = 222.6

Simplifying the equation:

1.06x = 222.6

Dividing both sides of the equation by 1.06:

x = 222.6 / 1.06

Now we can calculate the value of x and then find the distance traveled by the first train.

Calculation

Let's calculate the value of x and the distance traveled by the first train.

Using the given equation, we have:

x = 222.6 / 1.06

Calculating the value of x:

x ≈ 210

Now we can find the distance traveled by the first train:

Distance traveled by the first train = (0.2x) × 5.3

Substituting the value of x:

Distance traveled by the first train ≈ (0.2 × 210) × 5.3

Calculating the distance:

Distance traveled by the first train ≈ 22.26 × 5.3

Distance traveled by the first train ≈ 117.978 km

Answer

The first train traveled approximately 117.978 km.

Please let me know if I can help you with anything else.