A large hose will fill a pool in 40 minutes while it takes a smaller hose 60 minutes to fill the same pool. The same pool requires 80 minutes to drain if the drain is open. Suppose one day both hoses are turned on, but by accident the drain was left open. How long would it take to fill the pool that day?

Question

A large hose will fill a pool in 40 minutes while it takes a smaller hose 60 minutes to fill the same pool. The same pool requires 80 minutes to drain if the drain is open. Suppose one day both hoses are turned on, but by accident the drain was left open. How long would it take to fill the pool that day?

I have tried the following
1/40+1/60-1/80=
1/40=1/60=1/x

Answer 1

I assume you are not a Calculus student...

rate water=water/minute
= pool/40min+pool/60min - pool/80min

=pool(1/40+1/60-1/80)
= pool (60+40-30)/2400=pool*(7/240)

now to fill the pool
is the inverse of this rate, or
240/7 min= about 34 min

Answer 2

this is just your classic work problem. You started out right, but then went off into the mists.

1/x = 1/40+1/60-1/80
1/x = 7/240
x = 240/7

Answer 3

To find out how long it would take to fill the pool when both hoses are turned on and the drain is left open, we need to calculate the combined rate of filling and draining. Let's break down the problem step by step:

1. Calculate the rate at which the large hose fills the pool: In 1 minute, the large hose fills 1/40th of the pool.

2. Calculate the rate at which the smaller hose fills the pool: In 1 minute, the smaller hose fills 1/60th of the pool.

3. Calculate the rate at which the drain empties the pool: In 1 minute, the drain empties 1/80th of the pool.

4. Find the combined rate of filling and draining: To calculate this, we'll subtract the rate at which the drain empties from the combined rate at which both hoses fill the pool. The combined filling rate is 1/40 + 1/60, and the draining rate is 1/80. Therefore, the combined rate becomes 1/40 + 1/60 - 1/80.

5. Simplify the combined rate: To add fractions, you need a common denominator. In this case, the least common denominator (LCD) is 240, which is a multiple of both 40 and 60. So, we can express the combined rate as (6 + 4 - 3)/240 = 7/240.

The result is that the combined rate of filling the pool and the draining rate is 7/240 per minute.

6. Determine how long it would take to fill the pool: We divide 1 (the entire pool) by the combined rate of 7/240. This is equivalent to multiplying 1 by the reciprocal of the combined rate, which gives us 240/7 minutes.

Therefore, it would take approximately 34.29 minutes (or about 34 minutes and 17 seconds) to fill the pool when both hoses are turned on and the drain is left open.