Answer:
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.
