Question

От пристани А к пристани В отправился с постоянной скоростью первый теплоход, а через 1 час после этого следом за ним со скоростью на 1 км/ч большей отправился второй. Расстояние между пристанями равно 420 км. Найдите скорость первого теплохода, если в пункт В оба теплохода прибыли одновременно. Ответ дайте в км/ч.

Answer 1

420/х-420/(х+1)=1
Х-скорость первого
Х+1- скорость второго
Вычитаем и получаем один час.
В итоге получим квадратное уравнение
Х^2+х-420=0
Дискриминант = 1681
Х= -(1+41)/2=20
Ответ:20

Answer 2

Problem Analysis

We are given that two boats, Boat A and Boat B, depart from Port A to Port B. Boat A travels at a constant speed, while Boat B departs 1 hour later and travels at a speed that is 1 km/h faster than Boat A. The distance between the ports is 420 km. We need to find the speed of Boat A.

Solution

Let's assume the speed of Boat A is x km/h. Since Boat B departs 1 hour later and travels at a speed that is 1 km/h faster than Boat A, the speed of Boat B is (x + 1) km/h.

We can use the formula distance = speed × time to calculate the time taken by each boat to travel from Port A to Port B.

The time taken by Boat A is (420 km) / (x km/h) = 420 / x hours.

The time taken by Boat B is (420 km) / ((x + 1) km/h) = 420 / (x + 1) hours.

Since both boats arrive at Port B at the same time, the time taken by Boat A is equal to the time taken by Boat B. Therefore, we can set up the equation:

420 / x = 420 / (x + 1)

To solve this equation, we can cross-multiply and simplify:

420(x + 1) = 420x

Simplifying further:

420x + 420 = 420x

We can see that the variable x cancels out, leaving us with:

420 = 420

This equation is true for any value of x. Therefore, the speed of Boat A can be any positive value.

In conclusion, the speed of the first boat, Boat A, can be any positive value.