at 10:00 AM pipe A began to fill an empty storage tank. At noon, pipe A failed and was closed. Pipe B was used to finish filling the tank. If pipe A needs 6 hours to fill the tank alone and pipe B needs 8 hours, at what time was the tank full?

Question

at 10:00 AM pipe A began to fill an empty storage tank. At noon, pipe A failed and was closed. Pipe B was used to finish filling the tank. If pipe A needs 6 hours to fill the tank alone and pipe B needs 8 hours, at what time was the tank full?

Answer 1

let 1 represent the task of completely filling the tank

rate of pipe A = 1/6
rate of pipe B = 1/8
combined rate = 1/6 + 1/8 = 7/24
After 2 hours tank was filled 2(7/24) or 7/12
which remains 5/12 is yet to be filled
t(1/8) = 5/12
t = 8(5/12) = 10/3 hours or 3 hours and 20 minutes needed after noon

so at 3:20 the tank is full

Answer 2

To solve this problem, we need to determine the rate at which each pipe fills the tank and then calculate the time required to fill the tank using both pipes.

Let's start by finding the rate at which each pipe fills the tank:

Pipe A: It can fill the tank in 6 hours. So, the rate at which pipe A fills the tank is 1/6 tank per hour.

Pipe B: It takes 8 hours for pipe B to fill the tank. Hence, the rate at which pipe B fills the tank is 1/8 tank per hour.

Now, we can determine the combined rate of pipe A and pipe B when used together:

Combined rate = Rate of pipe A + Rate of pipe B

Combined rate = (1/6) + (1/8) = (4/24) + (3/24) = 7/24 tank per hour

We know that from 10:00 AM to noon (2 hours), only pipe A was used. So, pipe A filled the tank for 2 hours at its rate of 1/6 tank per hour:

Tank filled by pipe A = 2 hours * (1/6 tank per hour) = 1/3 tank

Since the tank is initially empty, after pipe A failed, the remaining fraction of the tank that needs to be filled is:

Remaining fraction of the tank = 1 - 1/3 = 2/3

Now, to find the time it takes both pipes to fill the remaining 2/3 of the tank, we can use their combined rate:

Time = (Remaining fraction of the tank) / (Combined rate)

Time = (2/3) / (7/24) = (2/3) * (24/7) = 48/21 = 2 2/7 hours

Therefore, the tank was full after 2 hours from 10:00 AM when pipe A was used, and an additional 2 2/7 hours when both pipes were used together.

To determine the final time when the tank was full, we can add the found time to the starting time of 10:00 AM.

Time = Starting time + Time to fill the tank

Time = 10:00 AM + 2 hours + 2 2/7 hours

Now, let's calculate the final time:

Time = 10:00 AM + 2 hours + 2 2/7 hours
= 10:00 AM + (2 + 2/7) hours
= 10:00 AM + (14/7 + 2/7) hours
= 10:00 AM + 16/7 hours
= 10:00 AM + 2 2/7 hours
≈ 10:00 AM + 2 hours + 17 minutes
≈ 12:17 PM

Therefore, the tank was full at approximately 12:17 PM.