Question

Из города А в город В выехал велосипедист. Спустя 0,8 часов вслед за ним выехал мотоциклист, скорость которого на 75 % больше скорости велосипедиста. Через 1,2 часа после своего выхода мотоциклист оказался впереди велосипедиста на 28 км. Найдите скорость мотоциклиста.

Answer 1

Скорость велосипедиста -х
скорость мотоциклиста х+0,75х= 1,75х
0,8 часа= 60х0,8=48минут
1,2час=60х1,2=72 минуты
48+72=120 минут =2 часа был в пути велосипедист
составим у-е
2х+28=1,2 * 1,75х
2х+28=2,1х
28=2,1-2х
28=0,1х
х=28:0,1
х=280км\час
280*0,75=210км\час
скорость мотоциклиста  280+210=490км\час
 

Answer 2

Problem Analysis

We are given that a cyclist left city A and after 0.8 hours, a motorcyclist left city A following the cyclist. The motorcyclist's speed is 75% faster than the cyclist's speed. After 1.2 hours from the start, the motorcyclist is 28 km ahead of the cyclist. We need to find the speed of the motorcyclist.

Solution

Let's assume the speed of the cyclist is x km/h. Since the motorcyclist's speed is 75% faster than the cyclist's speed, the speed of the motorcyclist can be expressed as 1.75x km/h.

We can use the formula distance = speed × time to calculate the distances traveled by the cyclist and the motorcyclist.

The distance traveled by the cyclist after 0.8 hours is 0.8x km.

The distance traveled by the motorcyclist after 1.2 hours is 1.2 × 1.75x km.

According to the problem, the motorcyclist is 28 km ahead of the cyclist after 1.2 hours. We can set up the following equation:

1.2 × 1.75x - 0.8x = 28

Simplifying the equation:

2.1x - 0.8x = 28

1.3x = 28

Solving for x:

x = 28 / 1.3

x ≈ 21.54

Therefore, the speed of the cyclist is approximately 21.54 km/h.

To find the speed of the motorcyclist, we can substitute the value of x into the expression for the motorcyclist's speed:

1.75x ≈ 1.75 × 21.54

≈ 37.69

Therefore, the speed of the motorcyclist is approximately 37.69 km/h.

Answer

The speed of the motorcyclist is approximately 37.69 km/h.