Question

Из пункта a в пункт b расстояние между которыми 32 км ,выехал велосипедист . через 0.5 часа ему навстречу выехал мотоциклист , они встретились через 0.5 часа после выезда мотоциклиста . скорость мотоциклиста на 28 км/час больше скорости велосипедиста . найти скорость каждого.

Answer 1

Х скорость велосипедиста
х+28 мотоциклиста
0,5х проехал велосипедист до выезда мотоциклиста
32-0,5х расстояние между ними в момент выезда мотоциклиста
х+х+28=2х+28 скорость сближения
0,5(2х+28)=32-0,5х
х+0,5х=32-14
1,5х=18
х=12км/час скорость велосипедиста
12+28=40км/час скорость мотоциклиста

Answer 2

Problem Analysis

We are given that the distance between point A and point B is 32 km. A cyclist starts from point A, and after 0.5 hours, a motorcyclist starts from point B and they meet after 0.5 hours. The speed of the motorcyclist is 28 km/h faster than the speed of the cyclist. We need to find the speed of each.

Solution

Let's assume the speed of the cyclist is x km/h. Then the speed of the motorcyclist is x + 28 km/h.

We can use the formula distance = speed × time to solve this problem.

The cyclist travels for 0.5 hours, so the distance traveled by the cyclist is 0.5x km.

The motorcyclist also travels for 0.5 hours, so the distance traveled by the motorcyclist is 0.5(x + 28) km.

Since they meet, the sum of their distances should be equal to the total distance between point A and point B, which is 32 km.

Therefore, we can write the equation:

0.5x + 0.5(x + 28) = 32

Now, let's solve this equation to find the value of x.

Calculation

0.5x + 0.5(x + 28) = 32

Simplifying the equation:

0.5x + 0.5x + 14 = 32

Combining like terms:

x + 14 = 32

Subtracting 14 from both sides:

x = 18

So, the speed of the cyclist is 18 km/h.

The speed of the motorcyclist is 18 + 28 = 46 km/h.

Answer

The speed of the cyclist is 18 km/h, and the speed of the motorcyclist is 46 km/h.