Question

Расстояние в 30 км один из велосипедистов проехал на 20 мин быстрее другого. Скорость первого велосипедиста была на 3 км/ч больше скорости второго. Какова Скорость каждого велосипедиста? Это задача была в алгебре ( 8 класс) . Прошу решить как 8 класс и не так иначе)

Answer 1

30 км - путь
20 мин = 1/3 часа
х - скорость велосипедиста
х+3 - скорость второго велосипедиста

путь/скорость=время

30/х-1/3=30/(х+3)
90-х/3х=30/(х+3)
(90-х)(х+3)=30*3х
90х+270-х²-3х=90х
-х²-3х+270=0
х=15 км/ч
х+3=18 км/ч

Answer 2

1) 20 мин = 1/3 часа
2) х - скорость первого велосипедиста
3) (х-3) - скорость второго
4) 30/(х-3) - 30/х = 1/3
90х-90х+270=х²-3х
х²-3х-270 =0
D= 9+1080 = 1089
х₁ = (3+√1089)/2 = (3 + 33)/2 = 36:2=18
х₁=18       км/час скорость первого велосипедиста
х₂=(3-33)/2 =- 15    не подходит
5) 18 - 3 = 15(км/час) скорость второго велосипедиста

Answer 3

Problem Analysis

We are given that two cyclists traveled a distance of 30 km. One cyclist traveled 20 minutes faster than the other. The speed of the first cyclist is 3 km/h faster than the speed of the second cyclist. We need to find the speed of each cyclist.

Solution

Let's assume the speed of the second cyclist is x km/h. Since the speed of the first cyclist is 3 km/h faster, the speed of the first cyclist is x + 3 km/h.

We know that time is equal to distance divided by speed. The time taken by the second cyclist to travel 30 km is given by:

Time taken by second cyclist = Distance / Speed = 30 / x

The time taken by the first cyclist is 20 minutes (or 1/3 hour) less than the time taken by the second cyclist:

Time taken by first cyclist = Time taken by second cyclist - 1/3 = 30 / x - 1/3

We can set up the equation:

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

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

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

Simplifying further:

30x + 90 - (1/3)x - 1 = 30x

Combining like terms:

(1/3)x = 89

Multiplying both sides by 3:

x = 267

Therefore, the speed of the second cyclist is 267 km/h.

The speed of the first cyclist is 3 km/h faster, so:

Speed of first cyclist = 267 + 3 = 270 km/h

Answer

The speed of the first cyclist is 270 km/h and the speed of the second cyclist is 267 km/h.

Note: The above solution assumes that the given information is accurate and there are no other factors affecting the speeds of the cyclists.