Question

Из двух пунктов между которыми по шоссе 120 км одновременно навстречу друг другу выехали мотоциклист и велосипедист Скорость мотоциклиста на 20 км в час больше скорости велосипедиста Сколько км проехал каждый из них если известно что они встретились через 3 часа?

Answer 1

Скорость сближения при движении навстречу - сумма скоростей.
1) Vc = V1 +V2 = 120 : 3 = 40 км/ч
Делим с разностью в 20 км/ч 
2) (40 - 20) : 2 = 10 км/ч - скорость  велосипедиста - ответ.
3) 10 + 20 = 30 км/ч - скорость мотоциклиста - ответ.

Answer 2

Problem Analysis

We are given that a motorcyclist and a cyclist started simultaneously from two points on a highway that are 120 km apart. The motorcyclist's speed is 20 km/h faster than the cyclist's speed. We need to determine how far each of them traveled if they met after 3 hours.

Solution

Let's assume the speed of the cyclist is x km/h. Since the motorcyclist's speed is 20 km/h faster, the speed of the motorcyclist is x + 20 km/h.

We know that distance = speed × time.

The distance traveled by the cyclist is x × 3 km, and the distance traveled by the motorcyclist is (x + 20) × 3 km.

To find the values of x and (x + 20), we can set up the following equation based on the fact that the total distance traveled by both of them is 120 km:

x × 3 + (x + 20) × 3 = 120

Simplifying the equation:

3x + 3x + 60 = 120

6x + 60 = 120

6x = 60

x = 10

Therefore, the speed of the cyclist is 10 km/h, and the speed of the motorcyclist is 30 km/h.

Substituting these values back into the distance formula:

The distance traveled by the cyclist is 10 × 3 = 30 km. The distance traveled by the motorcyclist is 30 × 3 = 90 km.

So, the cyclist traveled 30 km, and the motorcyclist traveled 90 km.

Answer

The cyclist traveled 30 km, and the motorcyclist traveled 90 km.

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