Question

Помогите очень срочно с задачкой Чтобы разгрузить баржу, два крана работали вместе 5 часов, и затем один первый работал еще 50 мин. Сколько часов потребуется первому крану, чтобы разгрузить баржу, если известно, что он может ее разгрузить на 2 часа быстрее, чем второй?

Answer 1

50мин=50/60=5/6ч
х-время быстрого (первого)
х+2-время медленного
1-груз
5(1/х+1/(х+2))+5/6*1/х=1 умножим на 6
30(1/х+1/(х+2))+5/х=6
30((х+2)/(х(х+2))+х/(х(х+2)))+5/х=6
30((х+2+х)/(х(х+2)))+5/х=6

30(2х+2)/(х(х+2))+5/х=6
30(2х+2)/(х(х+2))+5/х-6=0
30(2х+2)/(х(х+2))+5(х+2)/(х(х+2))-6х(х+2)/(х(х+2))=0
(30(2х+2)+5(х+2)-6х(х+2))/(х(х+2))=0
(60х+60+5х+10-6х²-12х)/(х(х+2))=0
(53х+70-6х²)/(х(х+2))=0
хне=0
хне=-2
53х+70-6х²=0
6х²-53х-70=0
D = (-53)² - 4·6·(-70) = 2809 + 1680 = 4489
x1 = (53 - √4489)/(2*6) = (53 - 67)/12 = -14/12 = -7/6 ≈ -1.17 - не подходит
x2 = (53 + √4489)/(2*6) = (53 + 67)/12 = 120/12 = 10 ч-столько часов потребуется первому крану, чтобы разгрузить баржу

Answer 2

Problem Analysis

To solve this problem, we need to determine how many hours the first crane will take to unload the barge if it can do it 2 hours faster than the second crane. We are given that both cranes worked together for 5 hours, and then the first crane worked for an additional 50 minutes.

Solution

Let's break down the problem step by step:

1. Convert the additional 50 minutes worked by the first crane into hours. Since there are 60 minutes in an hour, 50 minutes is equal to 50/60 = 5/6 hours.

2. Calculate the total time worked by both cranes together. We are given that they worked together for 5 hours, so the total time worked by both cranes is 5 + 5/6 = 5 5/6 hours.

3. Determine the time it takes for the second crane to unload the barge. Since the first crane can do it 2 hours faster than the second crane, the second crane takes x hours to unload the barge.

4. Calculate the time it takes for the first crane to unload the barge. Since the first crane is 2 hours faster than the second crane, the first crane takes x - 2 hours to unload the barge.

5. Set up an equation using the total time worked by both cranes. The equation is: (x - 2) + x = 5 5/6.

6. Solve the equation to find the value of x, which represents the time it takes for the second crane to unload the barge.

Let's solve the equation:

(x - 2) + x = 5 5/6

2x - 2 = 5 5/6

2x = 5 5/6 + 2

2x = 35/6 + 12/6

2x = 47/6

x = (47/6) / 2

x = 47/12

x ≈ 3.92

Therefore, the second crane takes approximately 3.92 hours to unload the barge.

7. Finally, calculate the time it takes for the first crane to unload the barge. Since the first crane is 2 hours faster than the second crane, it takes approximately 3.92 - 2 = 1.92 hours for the first crane to unload the barge.

Answer

The first crane will take approximately 1.92 hours to unload the barge.

Please note that the calculations are approximate due to rounding.

Let me know if you need any further assistance!

Answer 3

Problem Analysis

To solve this problem, we need to determine the amount of time it will take for the first crane to unload the barge, given that it can unload the barge 2 hours faster than the second crane. We are given that both cranes worked together for 5 hours, and then the first crane continued working for an additional 50 minutes.

Solution

Let's break down the problem step by step:

1. Calculate the total time worked by both cranes together: - The first crane worked for 5 hours. - The second crane's time is unknown.

2. Calculate the time worked by the first crane alone: - The first crane worked for an additional 50 minutes after the 5 hours of joint work. - Convert 50 minutes to hours: 50 minutes ÷ 60 minutes/hour = 0.83 hours.

3. Calculate the time worked by the second crane alone: - The total time worked by both cranes together is 5 hours. - Subtract the time worked by the first crane alone (5 hours + 0.83 hours) from the total time worked by both cranes together to find the time worked by the second crane alone.

4. Calculate the time it takes for the first crane to unload the barge: - The first crane can unload the barge 2 hours faster than the second crane. - Subtract 2 hours from the time worked by the second crane alone to find the time it takes for the first crane to unload the barge.

Let's calculate the solution using the given information:

1. Total time worked by both cranes together: 5 hours. 2. Time worked by the first crane alone: 5 hours + 0.83 hours = 5.83 hours. 3. Time worked by the second crane alone: Total time worked by both cranes together - Time worked by the first crane alone. 4. Time it takes for the first crane to unload the barge: Time worked by the second crane alone - 2 hours.

Let's calculate the solution:

1. Total time worked by both cranes together: 5 hours. 2. Time worked by the first crane alone: 5 hours + 0.83 hours = 5.83 hours. 3. Time worked by the second crane alone: 5 hours - 5.83 hours = -0.83 hours. - Note: The negative value indicates that the second crane did not work alone. 4. Time it takes for the first crane to unload the barge: -0.83 hours - 2 hours = -2.83 hours. - Note: The negative value indicates that the first crane cannot unload the barge.

Answer

Based on the given information, it is not possible for the first crane to unload the barge because the calculated time is negative (-2.83 hours).