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luis83113
04.06.2020 •
Mathematics
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?
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Ответ:
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.
Ответ:
Option C -![128 + 8.50x + 9.50y + 10z](/tpl/images/0475/6179/99aa4.png)
Step-by-step explanation:
Given : The Jones family plans a trip to the amusement park a purchase a family package for $128.00. They also want to buy lunch and souvenir cups. The chicken platter costs $8.50 each and the burger platter costs $9.50 each. The souvenir cups each cost $10.00
To find : Which of the following algebraic expressions can be used to describe the amount of money the Jones family will spend, before sales tax, based on the number of each meal and souvenir cups purchased?
Solution :
Let x represent the number of chicken platters.
Let y represents the number of burger platters.
Let z represent the number of souvenir cups.
A family package cost is $128.00.
The chicken platter costs $8.50 each
The cost of x chicken platter =![8.50x](/tpl/images/0475/6179/130f7.png)
The burger platter costs $9.50 each.
The cost of y burger platter =![9.50y](/tpl/images/0475/6179/ec084.png)
The souvenir cups each cost $10.00
The cost of z souvenir cups =![10z](/tpl/images/0475/6179/45e11.png)
Therefore, Total they spend is![128 + 8.50x + 9.50y + 10z](/tpl/images/0475/6179/99aa4.png)
Hence, Option C is correct.