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 had 22 m to the finish. At what distance was the race held?

Explanation:

Let distance be x meters

Fist statement:

Artur distance = x

Olga = x-15

Wiktor = x-35

Since they are going at constant speed, time is constant for all 3.

Their speed = distance/time

x/t, (x-15) / t, (x-35) / t respectively

Second statement:

Olga distance = x

Wiktor distance = x-22

Their Time is constant:

If it takes (x-15) in t secs,

for x meters will take = xt / (x-15)

Olga and wiktor respectively: xt / (x-15), xt / (x-15) respectively

Their speed:

Speed = distance/time

Olga = (x-15) / t,

Wiktor = (x-22) (x-15) / (xt)

Since speed is constant

Speed for Wiktor in both cases:

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

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

x² - 35x = x² - 15x - 22x + 330

-35x = - 37x + 330

2x = 330

x = 165m

Race held at 165m distance.