Question

Две команды лыжников шли навстречу друг другу с одинаковой скоростью. Первая команда прошла до встречи 40км за 4ч, а вторая команда прошла 20км. Сколько времени в пути была вторая команда? Решить задачу 3мя арифметическими способами

Answer 1

Problem Analysis

We are given that two teams of skiers are moving towards each other at the same speed. The first team travels 40 km in 4 hours before they meet, while the second team travels 20 km. We need to find the time it took for the second team to travel the given distance.

Solution 1: Using the formula Distance = Speed × Time

We can use the formula Distance = Speed × Time to find the time it took for the second team to travel 20 km. Since both teams are moving at the same speed, we can assume that the speed is constant for both teams.

Let's denote the speed of each team as s and the time taken by the second team as t.

For the first team: Distance = Speed × Time 40 km = s × 4 hours

For the second team: Distance = Speed × Time 20 km = s × t hours

Since the speed is the same for both teams, we can equate the two expressions: 40 km = 20 km × t hours

Now we can solve for t: t = 40 km / 20 km t = 2 hours

Therefore, the second team took 2 hours to travel the given distance.

Solution 2: Using the formula Time = Distance / Speed

Alternatively, we can use the formula Time = Distance / Speed to find the time it took for the second team to travel 20 km.

For the first team: Time = Distance / Speed 4 hours = 40 km / s

For the second team: Time = Distance / Speed t hours = 20 km / s

Since the speed is the same for both teams, we can equate the two expressions: 4 hours = 20 km / s

Now we can solve for t: t = 4 hours × (20 km / 40 km) t = 4 hours × 0.5 t = 2 hours

Therefore, the second team took 2 hours to travel the given distance.

Solution 3: Using the relative speed of the two teams

Another way to solve this problem is by considering the relative speed of the two teams. Since they are moving towards each other, their relative speed is the sum of their individual speeds.

Let's denote the speed of each team as s and the time taken by the second team as t.

For the first team: Distance = Speed × Time 40 km = s × 4 hours

For the second team: Distance = Speed × Time 20 km = s × t hours

Since the teams are moving towards each other, their relative speed is the sum of their individual speeds: Relative Speed = Speed of first team + Speed of second team Relative Speed = s + s = 2s

We can now use the formula Time = Distance / Speed to find the time taken by the second team: t hours = 20 km / (2s)

Since the speed is the same for both teams, we can simplify the expression: t hours = 10 km / s

Now we can substitute the value of s from the equation for the first team: t hours = 10 km / (40 km / 4 hours) t hours = 10 km / (10 km/h) t hours = 1 hour

Therefore, the second team took 1 hour to travel the given distance.

Conclusion

Using any of the three methods, we find that the second team took either 2 hours or 1 hour to travel the given distance of 20 km.