Question

Из деревень Орловка и вороново в 11 ч утра выехали навстречу друг другу велосипедист и мотоциклист. Они встретились в 11 ч 42 мин. Мотоциклист за час проезжает на 29.4 км больше, чем велосипедист. Найдите скорости велосипедиста и мотоциклиста, если расстояние между деревнями 44.1 км

Answer 1

Выехали в 11 часов, встретились  в 11 ч 42 мин. Значит . в пути были 42 мин= 42/60 ч= 0.7 ч
Пусть  х км/ч - скорость велосипедиста,
тогда х+ 29,4  км/ ч скорость мотоциклиста.
           (х+ х+ 29,4) км/ ч - скорость сближения,
          (х+ х+ 29,4)* 0,7 км - расстояние.
По условию - это 44,1 км.
(х+ х+ 29,4)* 0,7=44,1
2х+29,4=44,1:0.7
2х+29,4=63
2х=63-29,4
2х=33,6
х=16,8
х+ 29,4=16,8+29,4=46,2
Ответ: СКОРОСТЬ ВЕЛОС. 16,8 КМ/Ч, СКОРОСТЬ МОТОЦ. 46,2 КМ/Ч

Answer 2

Problem Analysis

We are given that a cyclist and a motorcyclist started from the villages of Orlovka and Voronovo respectively at 11:00 AM and met each other at 11:42 AM. The motorcyclist travels 29.4 km more than the cyclist in one hour. We need to find the speeds of the cyclist and the motorcyclist, given that the distance between the villages is 44.1 km.

Solution

Let's assume the speed of the cyclist is x km/h and the speed of the motorcyclist is y km/h.

We know that the motorcyclist travels 29.4 km more than the cyclist in one hour. This can be expressed as:

y - x = 29.4 ... (Equation 1)

We also know that the total time taken by both the cyclist and the motorcyclist to meet each other is 42 minutes, which is equal to 42/60 = 0.7 hours.

The distance traveled by the cyclist in this time is x * 0.7 km, and the distance traveled by the motorcyclist is y * 0.7 km.

Since they meet each other, the sum of their distances traveled must be equal to the total distance between the villages, which is 44.1 km. This can be expressed as:

x * 0.7 + y * 0.7 = 44.1 ... (Equation 2)

We now have a system of two equations (Equation 1 and Equation 2) that we can solve to find the values of x and y.

Let's solve the system of equations:

From Equation 1, we can express y in terms of x:

y = x + 29.4

Substituting this value of y into Equation 2:

x * 0.7 + (x + 29.4) * 0.7 = 44.1

Simplifying the equation:

0.7x + 0.7x + 20.58 = 44.1

1.4x = 44.1 - 20.58

1.4x = 23.52

x = 23.52 / 1.4

x ≈ 16.8

Substituting the value of x back into Equation 1 to find y:

y = 16.8 + 29.4

y ≈ 46.2

Therefore, the speed of the cyclist is approximately 16.8 km/h and the speed of the motorcyclist is approximately 46.2 km/h.

Answer

The speed of the cyclist is approximately 16.8 km/h and the speed of the motorcyclist is approximately 46.2 km/h.