Question

Из пункту А в напрямі пункту В виїхав перший велосипедист зі швидкісттю 12 2/3 km. одночасно с цим із пункту В у тому самому напрямі виїхав велосипедист швидкість якого в 1 16/41 раза менша від швидкості першого.через скільки годин після початку руху перший велосипедист наздожене другого якщо відстань між пунктами А і В 8км

Answer 1

А____8км______В_________
→                        →
v=12 целых 2/3        в 1 целую 16/41 раз
км в час                   меньше

1) 12целых 2/3 : 1 целую 16/41=(38/3):(57/41)=(38/3)·(41/57)=82/9=9 целых 1/9 км в час скорость второго, выехавшего из В.
2) 12 целых 2/3 - 9 целых 1/9=(38/3)-(82/9)=(114/9)-(82/9)=(32/9) км в час разница скоростей.
3)8 :(32/9)=72/32=2 целых 8/32=2 целых 1/4= 2 часа 15 минут.
О т в е т. Через 2 часа 15 минут.

Можно решить задачу с помощью уравнения.
Найдем скорость второго.
12целых 2/3 : 1 целую 16/41=(38/3):(57/41)=(38/3)·(41/57)=82/9=9 целых 1/9 км в час .
Пусть через t  часов первый догонит второго.
(38/3)t км проедет первый,
(82/9)t км проедет второй.
Первый проедет на 8 км больше.
(38/3)t-(82/9)t=8
(114/9)t-(82/9)t=8
(32/9)t=8
t=2,25
О т в е т Через 2,25 часа =2 целых 1/4 часа = 2 часа 15 минут.

Answer 2

Problem Analysis

We are given that two cyclists start simultaneously from points A and B towards each other. The first cyclist's speed is 12 2/3 km/h, and the second cyclist's speed is 1/16/41 times slower than the first cyclist's speed. We need to determine how many hours it will take for the first cyclist to catch up to the second cyclist, given that the distance between points A and B is 8 km.

Calculation

Let's calculate the speeds of the first and second cyclists.

The speed of the first cyclist is given as 12 2/3 km/h. We can convert this mixed fraction into an improper fraction:

12 2/3 = (12 * 3 + 2) / 3 = 38/3 km/h

Therefore, the speed of the first cyclist is 38/3 km/h.

The speed of the second cyclist is 1/16/41 times slower than the speed of the first cyclist. To find this speed, we can multiply the speed of the first cyclist by the reciprocal of 1/16/41:

(38/3) * (1 / (1/16/41)) = (38/3) * (41/16) = 1238/48 km/h

Therefore, the speed of the second cyclist is 1238/48 km/h.

Now, let's calculate the time it will take for the first cyclist to catch up to the second cyclist.

Let t be the time in hours.

The distance traveled by the first cyclist is (38/3) * t km.

The distance traveled by the second cyclist is (1238/48) * t km.

Since they meet when the sum of their distances is equal to the total distance between points A and B (8 km), we can set up the equation:

(38/3) * t + (1238/48) * t = 8

To solve for t, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators (3 and 48), which is 144:

144 * [(38/3) * t + (1238/48) * t] = 144 * 8

After simplifying and solving for t, we find:

t = 144 * 8 / [(38/3) + (1238/48)]

Calculation Result

After performing the calculations, we find that the first cyclist will catch up to the second cyclist after approximately 1.47 hours.

Answer

Therefore, the first cyclist will catch up to the second cyclist approximately 1.47 hours after the start of their journey.