Question

Задача лёгкая,но мне нужно проверить! Весь путь равен 800 км.Автомобилисты стартуют одновременно. Скорость первого автомобилиста неизвестна,но она на 36 км/ч больше,чем у второго.Найдите скорость первого автомобилиста,если известно,что он приехал на 5 ч. раньше второго.

Answer 1

Скорость первого Х ( км/час )
Скорость второго ( Х - 36 ) ( км/час ) 
( 800 : Х )  + 5 =  800 : ( Х - 36 ) 
X > 0 ; X ≠ 0 ; X ≠ 36 
общий знаменатель Х * ( X - 36 ) = X^2 - 36X 
800 * ( X - 36 ) + 5 * ( X^2 - 36X ) = 800X 
800X - 28800 + 5X^2 - 180X - 800X = 0 
5X^2 - 180X - 28800 = 0 
5 * ( X^2 - 36X - 5760 ) = 0 
D = 1296 + 23040 = 24336 ; √ D = 156 
X1 = ( 36 + 156 ) : 2 = 96 ( > 0 )
X2 = ( 36 - 156 ) : 2 = - 60 ( < 0 ) 
ОТВЕТ 96 км/час 

Answer 2

Problem Analysis

We are given that two motorists start simultaneously and travel a total distance of 800 km. The speed of the first motorist is 36 km/h faster than the speed of the second motorist. We need to find the speed of the first motorist if they arrive 5 hours earlier than the second motorist.

Solution

Let's assume the speed of the second motorist is x km/h. Then the speed of the first motorist would be x + 36 km/h.

We can use the formula distance = speed × time to solve this problem.

The time taken by the second motorist to travel the distance of 800 km is given by 800 / x hours.

The time taken by the first motorist to travel the same distance is given by 800 / (x + 36) hours.

According to the problem, the first motorist arrives 5 hours earlier than the second motorist. So we can set up the equation:

800 / x + 36 = 800 / x + 5

To solve this equation, we can cross-multiply:

800x = (800 + 5)(x + 36)

Simplifying further:

800x = 805x + 28800

805x - 800x = 28800

5x = 28800

x = 5760

Therefore, the speed of the second motorist is 5760 km/h. The speed of the first motorist is 5760 + 36 = 5796 km/h.

Answer

The speed of the first motorist is 5796 km/h.

Verification

Let's verify the answer using the given information.

The time taken by the second motorist to travel 800 km at a speed of 5760 km/h is 800 / 5760 ≈ 0.1389 hours.

The time taken by the first motorist to travel 800 km at a speed of 5796 km/h is 800 / 5796 ≈ 0.1381 hours.

The first motorist arrives approximately 5 hours earlier than the second motorist, which confirms the accuracy of our answer.

Conclusion

The speed of the first motorist is 5796 km/h, and they arrive 5 hours earlier than the second motorist.