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Two hoses are pouring water into an empty pool. Hose 1 alone would fil
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27 Feb 2023, 02:59
27 Feb 2023, 02:59
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Two hoses are pouring water into an empty pool. Hose 1 alone would fill up the pool in 6 hours. Hose 2 alone would fill up the pool in 4 hours. How long would it take for both hoses to fill up two-thirds of the pool?
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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Re: Two hoses are pouring water into an empty pool. Hose 1 alone would fil
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02 Mar 2023, 00:53
02 Mar 2023, 00:53
1
Expert Reply
Let's start by finding the individual rates at which each hose fills up the pool.
Hose 1 fills the pool in 6 hours, so its filling rate is:
Rate of Hose 1 = 1 pool / 6 hours = 1/6 pools per hour
Similarly, Hose 2 fills the pool in 4 hours, so its filling rate is:
Rate of Hose 2 = 1 pool / 4 hours = 1/4 pools per hour
When both hoses are used together, their filling rates add up. So, the combined filling rate of both hoses is:
Combined rate = Rate of Hose 1 + Rate of Hose 2
Combined rate = 1/6 + 1/4
Combined rate = 5/12 pools per hour
Now, let's determine how long it would take for both hoses to fill two-thirds of the pool. We can use the formula:
Time = Amount of work to be done / Rate of work
Here, the amount of work to be done is 2/3 of the pool, and the rate of work is 5/12 pools per hour. So, we get:
Time = (2/3) / (5/12)
Time = (2/3) * (12/5)
Time = 8/5
Time = 1.6 hours
Therefore, it would take both hoses approximately 1.6 hours (or 1 hour and 36 minutes) to fill up two-thirds of the pool.
Hose 1 fills the pool in 6 hours, so its filling rate is:
Rate of Hose 1 = 1 pool / 6 hours = 1/6 pools per hour
Similarly, Hose 2 fills the pool in 4 hours, so its filling rate is:
Rate of Hose 2 = 1 pool / 4 hours = 1/4 pools per hour
When both hoses are used together, their filling rates add up. So, the combined filling rate of both hoses is:
Combined rate = Rate of Hose 1 + Rate of Hose 2
Combined rate = 1/6 + 1/4
Combined rate = 5/12 pools per hour
Now, let's determine how long it would take for both hoses to fill two-thirds of the pool. We can use the formula:
Time = Amount of work to be done / Rate of work
Here, the amount of work to be done is 2/3 of the pool, and the rate of work is 5/12 pools per hour. So, we get:
Time = (2/3) / (5/12)
Time = (2/3) * (12/5)
Time = 8/5
Time = 1.6 hours
Therefore, it would take both hoses approximately 1.6 hours (or 1 hour and 36 minutes) to fill up two-thirds of the pool.
gmatclubot
Re: Two hoses are pouring water into an empty pool. Hose 1 alone would fil [#permalink]
02 Mar 2023, 00:53
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