Artur, Olga i Wiktor uczestniczyli w wyścigu. Wystartowali z tego samego miejsca, w tym samym momencie i biegną ze stałymi prędkościami. Gdy Artur ukończył bieg, Olga miała 15 m do mety, a Wiktor miał 35 m. Gdy Olga ukończyła bieg, Wiktorowi pozostały 22 m do mety. Na jakim dystansie został rozegrany wyścig?

165m

Question:

Artur, Olga and Wiktor participated in the race. They started from the same place at the same time and run at constant speeds. When Artur finished the race, Olga was 15 m to the finish,

and Wiktor was 35 m. When Olga finished the race, Wiktor remained 22 m to the finish. At what distance was the race held?

Step-by-step explanation:

Let Artur distance covered be =>x

When Artur covered distance x:

Olga was 15m from x

Olga = x - 15

Wiktor was 35m from x

Wiktor = x - 35

When Olga covered distance x:

Wiktor was 22m from x

The ratio of Olga to Wiktor:

(x-15)/(x-35) = x/(x-22)

Cross multiply

(x-15)(x-22) = x(x-35)

x² - 15x - 22x + 330 = x² - 35x

x² -37x +330 - x² + 35x = 0

-2x = -330

x = (-330)/(-2)

x = 165m

The race held at 165m distance

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign