Question

Чебурашка может разгрузить машину апельсинов за 6 часов, а Гена за 4 часа. Чебурашка проработал 2 часа, а затем ему на помощь пришел Гена, за сколько часов они разгрузили машину?

Answer 1

1/6-в час Чебурашка,1/4- в час крокодил, 1/6+1/4=5/12-в час вместе
1/6*2=1/3 погрузил Чебурашка за 2ч
1-1/3=2/3-загрузили вместе
2/3 : 5/12=2/3*12/5=8/5=1,6ч-грузили вместе
1,6+2=3,6ч-всего загружалась машина

Answer 2

Problem Analysis

We are given that Cheburashka can unload a truck of oranges in 6 hours, while Gena can do it in 4 hours. Cheburashka works for 2 hours and then Gena joins him. We need to determine how long it takes for them to unload the truck together.

Solution

To solve this problem, we can use the concept of work rates. The work rate is defined as the amount of work done per unit of time. If we let the work rate of Cheburashka be represented by C (in units of truckloads per hour) and the work rate of Gena be represented by G (in units of truckloads per hour), then we can set up the following equation:

2C + (x - 2)G = 1

Here, x represents the total time it takes for Cheburashka and Gena to unload the truck together. The left side of the equation represents the work done by Cheburashka in 2 hours (2C) plus the work done by Gena in (x - 2) hours ((x - 2)G), which should equal 1 truckload (since they are unloading the entire truck).

To solve for x, we can substitute the given work rates of Cheburashka and Gena into the equation and solve for x.

Calculation

Given: - Cheburashka's work rate: 1 truckload per 6 hours - Gena's work rate: 1 truckload per 4 hours

Substituting these values into the equation, we get:

2(1/6) + (x - 2)(1/4) = 1

Simplifying the equation, we have:

1/3 + (x - 2)/4 = 1

Multiplying through by 12 to eliminate the fractions, we get:

4 + 3(x - 2) = 12

Expanding and simplifying, we have:

4 + 3x - 6 = 12

3x - 2 = 12

3x = 14

x = 14/3

Therefore, it takes Cheburashka and Gena 14/3 hours to unload the truck together.

Answer

Cheburashka and Gena will unload the truck together in 14/3 hours.

Verification

To verify the answer, we can substitute the value of x back into the equation and check if it satisfies the equation:

2C + (x - 2)G = 1

Substituting x = 14/3, C = 1/6, and G = 1/4, we have:

2(1/6) + (14/3 - 2)(1/4) = 1

Simplifying the equation, we get:

1/3 + (2/3)(1/4) = 1

1/3 + 1/6 = 1

2/6 + 1/6 = 1

3/6 = 1

1/2 = 1

The equation is satisfied, which verifies that the answer is correct.

Conclusion

Cheburashka and Gena will unload the truck together in 14/3 hours.