Question

Один комбайнер может убрать урожай пшеницы с участка на 24 часа быстрее, чем другой. При совместной работе двух комбайнов они закончат уборку урожая за 35 часов. Сколько времени потребуется каждому комбайнеру, чтобы одному убрать урожай?

Answer 1

х время работы 1 комбайнёра

х+24 время работы 2 комбайнёра

1/х часть урожая будет убрана за 1 час 1 комбайнёром

1/х+24 часть урожая будет убрана 2 комбайнёром

1/35 часть работы будет убрана двумя комбайрёрами за 1 час

1/х+1/х+24=1/35

х^2-46х-840=0

d=5476

х1=-14

х2=60 часов потребуется 1 комбайнёру

60+24=84 часа потребуется 2 комбайнёру 

Answer 2

Problem Analysis

We are given that one harvester can harvest a wheat field 24 hours faster than another harvester. When these two harvesters work together, they can complete the harvest in 35 hours. We need to determine how long it would take each harvester to complete the harvest individually.

Solution

Let's assume that the slower harvester takes x hours to complete the harvest. Since the faster harvester can complete the harvest 24 hours faster, it would take (x - 24) hours for the faster harvester to complete the harvest.

When the two harvesters work together, they can complete the harvest in 35 hours. This means that their combined work rate is 1/35 of the field per hour. We can set up the following equation based on their individual work rates:

1/x + 1/(x - 24) = 1/35

To solve this equation, we can multiply through by the least common multiple of the denominators, which is 35x(x - 24):

35(x - 24) + 35x = x(x - 24)

Simplifying the equation:

35x - 840 + 35x = x^2 - 24x

Combining like terms:

70x - 840 = x^2 - 24x

Rearranging the equation:

x^2 - 94x + 840 = 0

Now we can solve this quadratic equation to find the value of x.

Quadratic Equation Solution

Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = -94, and c = 840:

x = (-(-94) ± √((-94)^2 - 4(1)(840))) / (2(1))

Simplifying:

x = (94 ± √(8836 - 3360)) / 2

x = (94 ± √5476) / 2

x = (94 ± 74) / 2

x = (94 + 74) / 2 or x = (94 - 74) / 2

x = 168 / 2 or x = 20 / 2

x = 84 or x = 10

Since the slower harvester cannot complete the harvest in 10 hours (as it would be faster than the faster harvester), the slower harvester takes 84 hours to complete the harvest. The faster harvester takes 84 - 24 = 60 hours to complete the harvest.

Answer

Therefore, the slower harvester takes 84 hours to complete the harvest, while the faster harvester takes 60 hours to complete the harvest.