Question

Расстояние от А до В равно 50 км.Из А в В поехал велосипедист,а через час 1,5ч следом за ним-мотоциклист,который обогнал велосипедиста и приехал в В на 1 ч раньше.Найти скорость каждого,если скорость мотоциклиста в 2,5 раза больше,чем велосипедиста.

Answer 1

T1, V1 -время и скорость велосипедиста,
t2, V2- время и скорость мотоциклиста,
S=50km путь
V2=2,5V1(km/h), t1-t2=2,5h
$S=V_{1}t_{1}=V_{2}t_{2}=>\\ V_{1}(t_{2}+2,5h)=2,5V_{1}t_{2}\\ t_{2}+2,5h=2,5t_{2}\\ 1,5t_{2}=2,5h;=> t_{2}= \frac{5}{3} (h)\\ t_{1}=2,5*t_{2}=2,5* \frac{5}{3}= \frac{25}{6}(h)\\ t_{1}-t_{2}= \frac{25}{6}- \frac{5}{3}= \frac{25-10}{6}= \frac{15}{6}= \frac{5}{2}=2,5 h\\ V_{2}= \frac{S}{t_{2}} = \frac{50}{ \frac{5}{3} }= \frac{50}{1} \frac{3}{5}=30(km/h)\\ v_{1}= \frac{S}{t_{1}}= \frac{50}{ \frac{25}{6} }= \frac{50}{25} \frac{6}{1}=12(km/h)$
Те-есть скорость мотоциклиста 30 км/час, а велосипедиста 12 км/час

Answer 2

Problem Analysis

We are given that the distance from point A to point B is 50 km. A cyclist starts from point A and after 1.5 hours, a motorcyclist starts from point A and overtakes the cyclist, arriving at point B 1 hour earlier than the cyclist. We need to find the speed of each person, given that the speed of the motorcyclist is 2.5 times greater than the speed of the cyclist.

Solution

Let's assume the speed of the cyclist is x km/h. Since the motorcyclist's speed is 2.5 times greater, the speed of the motorcyclist is 2.5x km/h.

We can use the formula distance = speed × time to calculate the time taken by each person.

The cyclist travels for 1.5 hours, so the distance covered by the cyclist is 1.5x km. The motorcyclist overtakes the cyclist and arrives at point B 1 hour earlier, so the distance covered by the motorcyclist is 50 km.

Now, we can set up the following equation based on the distances covered by each person:

1.5x + 50 = 2.5x

Simplifying the equation, we get:

50 = 2.5x - 1.5x

50 = 1x

Therefore, the speed of the cyclist is 50 km/h and the speed of the motorcyclist is 2.5 times greater, which is 125 km/h.

Answer

The speed of the cyclist is 50 km/h and the speed of the motorcyclist is 125 km/h.

Explanation

According to the given information, the distance from point A to point B is 50 km. The cyclist starts from point A and travels for 1.5 hours. The motorcyclist starts from point A 1.5 hours later and overtakes the cyclist, arriving at point B 1 hour earlier than the cyclist.

To find the speed of each person, we can use the formula distance = speed × time. Let's calculate the distance covered by each person:

- The cyclist travels for 1.5 hours, so the distance covered by the cyclist is 1.5 × speed of the cyclist. - The motorcyclist overtakes the cyclist and arrives at point B 1 hour earlier, so the distance covered by the motorcyclist is 50 km.

Setting up the equation based on the distances covered by each person:

1.5 × speed of the cyclist + 50 = 50

Simplifying the equation:

1.5 × speed of the cyclist = 50 - 50

1.5 × speed of the cyclist = 0

Dividing both sides of the equation by 1.5:

speed of the cyclist = 0 / 1.5

speed of the cyclist = 0

This means that the speed of the cyclist is 0 km/h. However, this doesn't make sense in the context of the problem. It seems there might be an error or inconsistency in the given information.

Please double-check the problem statement or provide any additional information if available, so that we can provide a more accurate solution.