Question

Из пункта А в пункт В, расстояние между которыми 13 км, вышел пешеход. Через полчаса навстречу ему из В в А выехал велосипедист, который ехал со скоростью, на 11 км/ч большей скорости пешехода. Найдите скорость велосипедиста, если известно, что они встретились в 5 км от пункта А.

Answer 1

Обозначим скорость пешехода v1 и скорость велосипедиста v2, тогда

5/v1=8/v2 +0.5
v2=v1+11
где 5/v1 -время до встречи пешехода и 8/v2   время до встречи велосипедиста
 v1=v2-11
5/(v2-11)=8/v2 +0.5
5v2-8(v2-11)=0.5v2(v2-11)
88-3v2=0.5v2²-0.5*11*v2
176-6v2=v2²-11v2
v2²-5v2-176=0
√D=√729=27
v2=0.5(5-27)<0 
V2=0.5(5+27)=16 км/ч

Ответ Скорость велосипедиста 16 км/ч

Answer 2

Problem Analysis

We are given that a pedestrian walks from point A to point B, a distance of 13 km. After half an hour, a cyclist starts from point B and travels towards point A at a speed 11 km/h faster than the pedestrian. We need to find the speed of the cyclist if they meet 5 km from point A.

Solution

Let's assume the speed of the pedestrian is x km/h. Since the cyclist is traveling 11 km/h faster, their speed is x + 11 km/h.

We know that the pedestrian has been walking for half an hour before they meet the cyclist. In that time, they have covered a distance of (1/2) * x km.

The distance covered by the cyclist is the remaining distance between the meeting point and point B, which is 13 - 5 = 8 km.

Now, we can set up the equation:

Distance covered by the pedestrian = Distance covered by the cyclist

[(1/2) * x] km = 8 km

Simplifying the equation:

(1/2) * x = 8

Multiplying both sides by 2:

x = 16

Therefore, the speed of the pedestrian is 16 km/h.

To find the speed of the cyclist, we add 11 km/h to the speed of the pedestrian:

Speed of the cyclist = 16 + 11 = 27 km/h

So, the speed of the cyclist is 27 km/h.

Answer

The speed of the cyclist is 27 km/h.