Question

Решите задачу! В первый день велосипедист проехал на 30 км больше, чем во второй. Какое расстояние он проехал за 2 дня, если на весь путь затрачено 5 часов, причем в первый день он ехал со скоростью 20 км/ ч, а во второй 15 км/ч.

Answer 1

Надо просто записать условие математическими формулами и решение станет очевидным.
Расстояние за второй день = x, время движения = t2.
Расстояние за первый день = x+30, время движения = t1.
Общее время t1+t2=5;
Общее расстояние S=x+(x+30); Выразим расстояние через скорость и время движения: x=15t2; x+30=20t1; Значит 15t2+30=20t1; при этом t1=5-t2; подставим: 15t2+30=20(5-t2); 15t2+20t2=100-30; 35t2=70; t2=2 ч. Значит t1=3 ч.
Получаем общее расстояние: S=15*2+20*3; S=90 км.

Answer 2

Problem Analysis

To solve this problem, we need to find the total distance traveled by the cyclist in two days. We are given that on the first day, the cyclist traveled 30 km more than on the second day. We are also given the speeds at which the cyclist traveled on each day, as well as the total time taken for the entire journey.

Solution

Let's assume that the distance traveled on the second day is x km. Since the distance traveled on the first day is 30 km more than on the second day, the distance traveled on the first day would be x + 30 km.

We can use the formula: distance = speed × time to calculate the time taken on each day.

On the first day: - Speed = 20 km/h - Time = distance / speed = (x + 30) / 20

On the second day: - Speed = 15 km/h - Time = distance / speed = x / 15

The total time taken for the entire journey is given as 5 hours. So, we can write the equation: (x + 30) / 20 + x / 15 = 5

To solve this equation, we can multiply through by the least common multiple (LCM) of 20 and 15, which is 60, to eliminate the denominators.

60 * [(x + 30) / 20] + 60 * [x / 15] = 5 * 60

Simplifying the equation: 3(x + 30) + 4x = 300 3x + 90 + 4x = 300 7x + 90 = 300 7x = 210 x = 30

Therefore, the distance traveled on the second day is 30 km. And the distance traveled on the first day is x + 30 = 30 + 30 = 60 km.

The total distance traveled in two days is 30 km + 60 km = 90 km.

Answer

The cyclist traveled a total distance of 90 km in two days.

Explanation

Let's verify the solution using the given information: - On the first day, the cyclist traveled at a speed of 20 km/h for a time of 60/20 = 3 hours. The distance covered is 20 km/h * 3 hours = 60 km. - On the second day, the cyclist traveled at a speed of 15 km/h for a time of 30/15 = 2 hours. The distance covered is 15 km/h * 2 hours = 30 km. - The total distance covered is 60 km + 30 km = 90 km.

The solution is consistent with the given information.