Question

Ваня и Оля дежурили в столовой туристического лагеря . Вдвоём они чистили 400 штук картофеля .Оля очищала 3 штуки в минуту,а Ваня-2,Ваня работал на 25 минутдольше Оли. Сколько времениони работали вместе?Запиши вопросы к действиям и дополни записи в решении.

Answer 1

1) Сколько Ваня чистил картошки в час?
2) Сколько Оля чистила картошки в час?
3) За сколько они вместе очищали 400 картошки?


1) 2•60=120 - Ваня очищал за час
2) 3•60=180 - Оля очищала за час
3) 120+180=300
400:300=1.3 часа им требовалось для прочистки 400 картошин

Answer 2

Problem Analysis

To solve this problem, we need to find the total time Vanya and Olya worked together to clean 400 potatoes. We are given that Olya cleans 3 potatoes per minute and Vanya cleans 2 potatoes per minute. Additionally, Vanya worked 25 minutes longer than Olya.

Solution

Let's break down the problem step by step:

1. Let's assume the time Olya worked is x minutes. 2. Since Vanya worked 25 minutes longer than Olya, Vanya worked for x + 25 minutes. 3. Olya cleaned 3 potatoes per minute, so in x minutes, she cleaned 3x potatoes. 4. Vanya cleaned 2 potatoes per minute, so in x + 25 minutes, he cleaned 2(x + 25) potatoes. 5. Together, they cleaned a total of 400 potatoes, so we can set up the equation: 3x + 2(x + 25) = 400. 6. Simplifying the equation, we get: 3x + 2x + 50 = 400. 7. Combining like terms, we have: 5x + 50 = 400. 8. Subtracting 50 from both sides, we get: 5x = 350. 9. Dividing both sides by 5, we find: x = 70.

Therefore, Olya worked for 70 minutes, and Vanya worked for 70 + 25 = 95 minutes.

To find the total time they worked together, we add their individual times: 70 + 95 = 165 minutes.

So, Vanya and Olya worked together for 165 minutes.

Answer

Vanya and Olya worked together for 165 minutes.

Questions to Consider

1. What is the given information in the problem? 2. How can we represent the time Olya worked and the time Vanya worked in terms of a variable? 3. How can we represent the number of potatoes cleaned by Olya and Vanya in terms of the variable? 4. What equation can we set up to represent the total number of potatoes cleaned? 5. How can we solve the equation to find the value of the variable? 6. How can we find the total time they worked together?