Question

Из двух пунктов, расстояние между которыми 117 км, одновременно навстречу друг другу выехали мотоциклист и велосипедист. Скорость мотоциклиста на 50 км/ч больше скорости велосипедиста. Сколько километров проехал каждый до встречи, если она произошла через 1,5 часа после начала движения?

Answer 1

117/1,5=78км/ч общая скорость

78-50=28 км/ч

28/2=14км/ч скорость велосипедиста

14+50=64 км/ч скорость мотоциклиста

14*1,5=21км проехал велосипедист

64*1,5=96км проехал мотоциклист

Answer 2

Problem Analysis

To solve this problem, we need to find the distances traveled by the motorcyclist and the cyclist before they meet. We know that the distance between them is 117 km and they meet 1.5 hours after starting their journey. Additionally, the motorcyclist's speed is 50 km/h faster than the cyclist's speed.

Calculating the Distances Traveled

Let's denote the speed of the cyclist as x km/h. Then the speed of the motorcyclist would be (x + 50) km/h.

The total distance traveled by both the motorcyclist and the cyclist is 117 km. We can use the formula: distance = speed * time

The time for both the motorcyclist and the cyclist is the same, as they meet at the same time. Therefore, we can calculate the distances traveled by each using the formula above.

Solution

Let's solve for the distances traveled by the motorcyclist and the cyclist.

The distance traveled by the motorcyclist is (x + 50) * 1.5 km, and the distance traveled by the cyclist is x * 1.5 km.

We can then solve for x using the equation (x + 50) * 1.5 + x * 1.5 = 117.

Calculating the Speeds

Once we find the value of x, we can calculate the distances traveled by the motorcyclist and the cyclist.

Let's proceed with the calculations.