Question

Из двух населенных пунктов одновременно навстречу друг другу выехали два велосипедиста.они встретились через 3 часа.в час один велосипедист проходит на 2 км больше другого. какова скорость каждого велосипедиста,если расстояние между населенными пунктами равно 66 км. решить системой уравнения

Answer 1

Держи, пишу без дано

Answer 2

Problem Analysis

We have two cyclists who start simultaneously from two different towns and meet each other after 3 hours. The speed of one cyclist is 2 km/h faster than the other. The distance between the towns is 66 km. We need to find the speed of each cyclist.

Solution

Let's assume the speed of the slower cyclist is v km/h. Then the speed of the faster cyclist would be v + 2 km/h.

We can use the formula distance = speed × time to create two equations based on the given information.

Equation 1: distance = speed × time for the slower cyclist Equation 2: distance = speed × time for the faster cyclist

We know that the distance between the towns is 66 km and the time taken to meet is 3 hours. Substituting these values into the equations, we get:

Equation 1: 66 = v × 3 Equation 2: 66 = (v + 2) × 3

Now we can solve this system of equations to find the values of v and v + 2.

Solving the System of Equations

Let's solve the system of equations using the substitution method.

From Equation 1, we have 66 = v × 3. Solving for v, we get v = 22.

Substituting the value of v into Equation 2, we get 66 = (22 + 2) × 3. Simplifying, we have 66 = 24 × 3.

Therefore, the speed of the slower cyclist is 22 km/h and the speed of the faster cyclist is 24 km/h.

Answer

The speed of the slower cyclist is 22 km/h and the speed of the faster cyclist is 24 km/h.

Verification

Let's verify the answer by checking if the distances covered by both cyclists in 3 hours match the given information.

The distance covered by the slower cyclist in 3 hours is 22 × 3 = 66 km. The distance covered by the faster cyclist in 3 hours is 24 × 3 = 72 km.

As the distance between the towns is 66 km, the answer is verified.