Question

Через первую трубу бак наполняется за 30 мин. За сколько минут наполняется бак через вторую трубу, если две трубы вместе наполняют его за 20 мин?

Answer 1

(x+30):2=20,

x+30=40,

x=10

Ответ: за 10 минут

Answer 2

#### Problem Analysis We are given that the first pipe can fill a tank in 30 minutes and the two pipes together can fill the tank in 20 minutes. We need to find out how long it would take for the second pipe to fill the tank on its own. #### Solution Let's assume that the second pipe can fill the tank in x minutes. From the given information, we know that the first pipe can fill the tank in 30 minutes. Therefore, in 1 minute, the first pipe can fill 1/30th of the tank. Similarly, we know that both pipes together can fill the tank in 20 minutes. Therefore, in 1 minute, both pipes together can fill 1/20th of the tank. To find out how long it would take for the second pipe to fill the tank on its own, we need to subtract the rate at which the first pipe fills the tank from the rate at which both pipes together fill the tank. Let's calculate the rates: - Rate of the first pipe = 1/30th of the tank per minute. - Rate of both pipes together = 1/20th of the tank per minute. To find the rate of the second pipe, we subtract the rate of the first pipe from the rate of both pipes together: Rate of the second pipe = Rate of both pipes together - Rate of the first pipe Rate of the second pipe = 1/20 - 1/30 Simplifying the expression: Rate of the second pipe = (3/60) - (2/60) Rate of the second pipe = 1/60th of the tank per minute. This means that the second pipe can fill 1/60th of the tank in 1 minute. To find out how long it would take for the second pipe to fill the tank on its own, we need to calculate the reciprocal of the rate of the second pipe: Time taken by the second pipe to fill the tank = 1 / (1/60) Simplifying the expression: Time taken by the second pipe to fill the tank = 60 minutes. #### Answer Therefore, the second pipe can fill the tank on its own in **60 minutes**. #### Sources: