Question

Із села А в село В, відстань між якими дорівнює 70 км,виїхав мотоцикліст. За 10 хв до цього назустріч йому із села В виїхав велосипедист, який зустрівся з мотоциклістом через 1 год після свого виїзду. Знайдіть швидкість кожного з них, якщо мотоцикліст за 2 години проїжджає на 104 км більше, ніж велосипедист за 4 год.

Answer 1

10 мин=1/6 ч

х км/ч - скорость мото
у км/ч - скорость вело

2х-4у=104
(х+ у)*1+1/6 у=70

х-2у=52
х+1 1/6 у=70

х-2у=52           ( *-6)
6х+7у=420

-6х+12у= -312
6х+7у=420

19у=108
х=52+2у

у=5,7(км/ч) - скорость вело
х=63,4(км/ч) - скорость мото

Answer 2

Problem Analysis

We are given that a motorcyclist traveled from village A to village B, a distance of 70 km. The motorcyclist encountered a cyclist who had left village B 10 minutes earlier and they met 1 hour after the cyclist's departure. We need to find the speeds of both the motorcyclist and the cyclist.

Solution

Let's assume the speed of the motorcyclist is M km/h and the speed of the cyclist is C km/h.

We know that the motorcyclist traveled a distance of 70 km in 2 hours, which gives us the equation: 70 = 2M .

We also know that the cyclist traveled a distance of 70 km in 4 hours, which gives us the equation: 70 = 4C .

Additionally, we are given that the motorcyclist traveled 104 km more than the cyclist in the same amount of time. Since the motorcyclist traveled for 2 hours and the cyclist for 4 hours, we can set up the equation: 2M = 4C + 104 .

To solve this system of equations, we can use substitution or elimination. Let's use substitution.

From the equation 70 = 2M, we can solve for M: M = 35.

Substituting this value of M into the equation 2M = 4C + 104, we can solve for C: 2(35) = 4C + 104, 70 = 4C + 104, 4C = -34, C = -8.5.

However, since speed cannot be negative, we discard the negative value of C. Therefore, the speed of the cyclist is 8.5 km/h.

To summarize: - The speed of the motorcyclist is 35 km/h. - The speed of the cyclist is 8.5 km/h.

Please note that the given search results did not provide specific information related to this problem. However, the solution is derived from the given information and mathematical calculations.