Question

Из пунктов и A,B расположенных на расстоянии 100 км, навстречу друг другу одновременно выехали два велосипедиста. Через 4 часа они встретились. После встречи скорость первого велосипедиста , едущего из A в B возросла на 5 км/ч, а скорость второго, едущего из B в A возросла на 10 км/ч. Известно, что первый велосипедист прибыл в пункт B на 1 час раньше, чем второй прибыл в пункт A Определить первоначальную скорость первого велосипедиста.

Answer 1

15 км/час. За 4 часа он проехал 6 км, а потом со скоростью 20 км/час проехал 4 км за 2часа. А второй велос-ист сначала 10км/ час

Answer 2

Problem Analysis

We have two cyclists starting from points A and B, which are 100 km apart. They start simultaneously and meet after 4 hours. After the meeting, the speed of the first cyclist traveling from A to B increases by 5 km/h, while the speed of the second cyclist traveling from B to A increases by 10 km/h. We need to determine the initial speed of the first cyclist.

Solution

Let's assume the initial speed of the first cyclist is x km/h. Since the distance between A and B is 100 km, the time taken by the first cyclist to travel from A to B at the initial speed is 100/x hours.

After the meeting, the first cyclist arrives at point B 1 hour earlier than the second cyclist arrives at point A. This means the second cyclist takes 100/(x+5) hours to travel from B to A.

We are given that the total time taken for the meeting is 4 hours. So, the time taken by the first cyclist to travel from A to the meeting point is 4 - 100/(x+5) hours.

Since the total distance traveled by the first cyclist is 100 km, we can set up the following equation:

100/x + 4 - 100/(x+5) = 4

Simplifying the equation, we get:

100/x - 100/(x+5) = 0

To solve this equation, we can find a common denominator and then solve for x.

Calculation

Let's solve the equation to find the initial speed of the first cyclist.

100/x - 100/(x+5) = 0

Multiplying both sides of the equation by x(x+5) to eliminate the denominators:

100(x+5) - 100x = 0

Expanding and simplifying the equation:

100x + 500 - 100x = 0

500 = 0

Since the equation simplifies to 500 = 0, there is no solution. This means there is no initial speed for the first cyclist that satisfies the given conditions.

Conclusion

Based on the given information, there is no initial speed for the first cyclist that satisfies the conditions of the problem.