Question

Используя одновременно два подьемных крана, баржу разгрузили за 6 часов. За какое время можно разгрузить эту баржу, каждым из кранов в отдельности, если первому на это потребуется на 9 часов меньше чем 2-му?

Answer 1

1 - вся работа по разгрузке баржи
За х часов разгрузит 2-й
За (х-9) часов разгрузит 1-й
1/6 - за 1 час разгрузят вместе
1/х - за 1 час разгрузит 2-й
1/(х-9) - за 1 час разгрузит 1-й
Составим уравнение:
1/х+1/(х-9)=1/6 (умножим на 6х(х-9))
6(х-9)+6х=х(х-9)
6х-54+6х=х2-9х
х2-9х-12х+54=0
х2-21х+54=0
D=21*21-4*54=441-216=225;   Корень из D=15
х"=(21-15):2=6:2=3 (не подходит по условию)
х=(21+15):2=36:2=18 (час) 2-й кран
х-9=18-9=9 (час) 1-й
Ответ:работая по отдельности, первый кран разгрузит баржу за 9 часов, а второй за 18 часов

Answer 2

Problem Analysis

We are given that a barge was unloaded using two cranes working simultaneously, and it took 6 hours to complete the unloading. We need to determine how long it would take each crane to unload the barge individually, given that the first crane takes 9 hours less than the second crane.

Solution

Let's assume that the time taken by the first crane to unload the barge is x hours. According to the given information, the second crane takes 9 hours more than the first crane, so the time taken by the second crane is (x + 9) hours.

To find the total time taken to unload the barge using both cranes, we can add the individual times: x + (x + 9) = 6

Simplifying the equation: 2x + 9 = 6 2x = 6 - 9 2x = -3 x = -3/2

The solution to the equation is x = -3/2, which is not a valid solution since time cannot be negative. Therefore, there is no valid solution to this problem.

Answer

There is no valid solution to the problem of unloading the barge individually using the two cranes, given that the first crane takes 9 hours less than the second crane.