Question

Мотоцикліст проїхав 40 км з пункту А в пункт В і повернувся назад. На зворотному шляху він зменшив швидкість на 10 км/год порівняно з початковою і витратив на подорож на 20 хв більше, ніж на шлях з пункту А в пункт В. Знайдіть початкову швидкість мотоцикліста (у км/год).

Answer 1

Можешь на русском языке ато не понятно

Answer 2

Problem Analysis

We are given that a motorcyclist traveled 40 km from point A to point B and then returned back. On the return journey, the motorcyclist reduced their speed by 10 km/h compared to the initial speed and took 20 minutes longer than the journey from point A to point B. We need to find the initial speed of the motorcyclist in km/h.

Solution

Let's assume the initial speed of the motorcyclist is v km/h.

The time taken to travel from point A to point B at speed v is given by: t1 = 40/v hours. (Since distance = speed × time)

On the return journey, the motorcyclist reduced their speed by 10 km/h, so the speed becomes v - 10 km/h.

The time taken to travel from point B to point A at speed v - 10 km/h is given by: t2 = 40/(v - 10) hours.

We are also given that the time taken on the return journey is 20 minutes (or 20/60 = 1/3 hours) longer than the time taken on the journey from point A to point B. So we have the equation: t2 = t1 + 1/3.

Substituting the values of t1 and t2, we can solve for v.

Calculation

Let's solve the equation t2 = t1 + 1/3 to find the value of v.

40/(v - 10) = 40/v + 1/3

Multiplying both sides of the equation by 3v(v - 10) to eliminate the denominators:

120v = 120(v - 10) + v(v - 10)

Expanding and simplifying:

120v = 120v - 1200 + v^2 - 10v

Rearranging the terms:

v^2 - 10v - 1200 = 0

Factoring the quadratic equation:

v^2 - 40v + 30v - 1200 = 0

v(v - 40) + 30(v - 40) = 0

(v + 30)(v - 40) = 0

So, v = -30 or v = 40.

Since the speed cannot be negative, the initial speed of the motorcyclist is 40 km/h.

Answer

The initial speed of the motorcyclist is 40 km/h.