Question

Расстояние в 30 км один из двух лыжников прошел на 20 минут быстрее другого. Скорость первого больше скорости второго на 3км/ч. Какова скорость каждого лыжника?

Answer 1

Пусть х - скорость 2-го лыжника. тогда х+3 скорость 1-го лыжника.
30/х-30/х+3=1/3
30(х+3)-30х/х(х+3)=1/3
90/х^2+3х=1/3
х^2+3х=270
х^2+3х-270=0
D=3^2+270*4=1089
х1,2=-3+-33/2
х1=-18
х2=15
х1 не удовлетворяет условию(скорость не может быть отрицательной). следовательно х=х2=15
а скорость первого лыжника=х+3=18

ответ:скорость первого = 18км/ч
второго = 15км/ч

Answer 2

Х-скорость 1,время 30/х
х-3-скорость 2,время 30/(х-3)
30/(х-3)-30/х=1/3
х²-3х-90(х-х+3)=0
х²-3х-270=0
х1+х2=3 и х1*х2=-270
х1=-15 не удов усл
х2=18км/ч-скорость 1
18-3=15км/ч-скорость 2

Answer 3

Problem Analysis

We are given that two skiers have covered a distance of 30 km, with one skier being 20 minutes faster than the other. The speed of the first skier is 3 km/h faster than the speed of the second skier. We need to find the speed of each skier.

Solution

Let's assume the speed of the slower skier is x km/h. Therefore, the speed of the faster skier would be x + 3 km/h.

We know that time is equal to distance divided by speed. The time taken by the slower skier to cover the distance of 30 km is given by:

Time taken by slower skier = Distance / Speed = 30 / x

The time taken by the faster skier to cover the same distance is given by:

Time taken by faster skier = Distance / Speed = 30 / (x + 3)

We are given that the faster skier is 20 minutes faster than the slower skier. Since 20 minutes is equal to 1/3 of an hour, we can set up the following equation:

Time taken by slower skier + 1/3 = Time taken by faster skier

Substituting the expressions for time taken by each skier, we get:

30 / x + 1/3 = 30 / (x + 3)

To solve this equation, we can cross-multiply and simplify:

30(x + 3) = 30x + 10

Simplifying further:

30x + 90 = 30x + 10

The 30x terms cancel out, leaving us with:

90 = 10

This equation is not possible to solve, as it leads to a contradiction. Therefore, there is no solution to this problem.

Conclusion

There is no solution to the problem, as the given information leads to a contradiction.