Question

Из пункта А в направлении пункта В выехал первый велосипедист со скоростью 12 целых две третьих. Одновременно из пункта В в том же направлении выехал второй велосипедист, скорость которого в 1 целую шестнадцать сорок первых меньше скорости первого. Через сколько часов после начала движения первый велосепедист дооогит второго, если расстояния между пунктами А и В равно 8 км?

Answer 1

Через 2часа он догонит его

Answer 2

Problem Analysis

We have two cyclists traveling from point A to point B. The first cyclist has a speed of 12 and two-thirds, and the second cyclist has a speed that is 1 and 16/40 less than the speed of the first cyclist. 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.

Solution

Let's start by converting the speeds of the cyclists into fractions. The first cyclist's speed is 12 and two-thirds, which can be written as 12 + 2/3 = 38/3. The second cyclist's speed is 1 and 16/40 less than the speed of the first cyclist, which can be written as (38/3) - (1 + 16/40) = (38/3) - (56/40) = (38/3) - (7/5) = (190/15) - (21/15) = 169/15.

Now, let's set up an equation to represent the distance traveled by each cyclist. Since both cyclists are traveling in the same direction, the equation will be:

(distance traveled by the first cyclist) = (distance traveled by the second cyclist) + 8

Let's assume that it takes t hours for the first cyclist to catch up to the second cyclist. The distance traveled by the first cyclist is (38/3) * t, and the distance traveled by the second cyclist is (169/15) * t. Substituting these values into the equation, we get:

(38/3) * t = (169/15) * t + 8

To solve for t, we can multiply both sides of the equation by 15 to eliminate the denominators:

15 * (38/3) * t = 15 * (169/15) * t + 15 * 8

Simplifying the equation, we have:

190t = 169t + 120

Subtracting 169t from both sides, we get:

21t = 120

Dividing both sides by 21, we find:

t = 120/21 = 40/7

Therefore, it will take the first cyclist 40/7 hours to catch up to the second cyclist.

Answer

It will take the first cyclist 40/7 hours to catch up to the second cyclist.