Question

велосипедист проехал 60 км из пункта А в пункт В с постоянной скоростью. назад из пункта В в пункт А он увеличил скорость на 10 км.ч и потратил на 60 мин меньше. Найти начальную скорость велосипеда

Answer 1

$\frac{60}{x}-\frac{60}{x+10}=1\\ x^2+10x-600=0\\ x_{1}=-30\\x_{2}=20$

20 км/ч

Answer 2

Problem Analysis

We are given that a cyclist traveled 60 km from point A to point B at a constant speed. On the return journey from point B to point A, the cyclist increased their speed by 10 km/h and spent 60 minutes less. We need to find the initial speed of the bicycle.

Solution

Let's assume the initial speed of the bicycle is x km/h.

On the first journey from point A to point B, the cyclist traveled 60 km at a constant speed of x km/h. Using the formula distance = speed × time, we can write the equation:

60 = x × t1 On the return journey from point B to point A, the cyclist increased their speed by 10 km/h. So, the speed on the return journey is (x + 10) km/h. The time taken for the return journey is 60 minutes less than the time taken for the first journey. We can write the equation:

60 = (x + 10) × (t1 - 60/60) Simplifying equation we get:

60 = (x + 10) × (t1 - 1)

Expanding the equation, we get:

60 = x × t1 + 10 × t1 - x - 10

Simplifying further, we get:

60 = x × t1 + 10 × t1 - x - 10

60 = (x + 10) × t1 - x - 10

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