Question

amin is using a hose to fill his new pool for the first time. he starts the hose at 10 pm and leaves it running all night. at 6 am he measures the depth and calculates that the pool is four sevenths full. at what time will his new pool be full?

Answer 1

Using proportional reasoning, it is determined that Amin's pool will be full by 12 pm (noon) if it has reached four sevenths capacity after 8 hours of filling with water at a constant rate.

Step-by-step explanation:

Amin has filled his pool to four sevenths of its capacity in 8 hours, from 10 pm to 6 am. Assuming the rate at which the pool is filling remains constant, we can calculate the remaining time to fill the pool completely.

Since it takes 8 hours to fill four sevenths of the pool, we can use the following proportion to find the total time (T) to fill the entire pool:

8 hours / (4/7) = T hours / 1

By cross-multiplying and solving for T, we find that:

T = 8 hours * (7/4) = 14 hours

Therefore, if the pool is already four sevenths full after 8 hours, it will take an additional 6 hours (14 hours - 8 hours) to fill the pool completely. If Amin checks the pool at 6 am, adding 6 hours to this time indicates the pool will be full by 12 pm (noon).