Question

jean and mark are going to fill a pool with 2 different sized hoses. Jean can fill the pool in 8 hours, while Mark can complete it in 12 hours. Their supervisor thinks that the job will take 10 hours to complete if they work together. Explain each step in solving the equation, and determine if the supervisor is correct or not.

Answer 1

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Calculate Jean's rate
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Jean takes 8 hours to fill the pool.
So in 1 hour, she can fill 1/8 of the pool

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Calculate Mark's rate
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Mark takes 12 hours to fill the pool.
So in 1 hour, he can fill 1/12 of the pool.

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Calculate their rate if they work together
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Jean = 1/8
Mark = 1/12
1/8 + 1/12 = 3/24 + 2/24 = 5/24 
They will fill 5/24 of the pool in 1 hour

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Find number of hours needed to fill up the pool
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I hour = 5/24 of the pool
1 ÷ 5/24 hour = 5/24 ÷ 5/24 of the pool
24/5 hour =  Whole pool

Whole pool = 24/5 hours 
Whole pool = 4 4/5 hours  or 4.8 hours

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Ans: The supervisor is not correct, it will take only 4.8 hours if both of them work together.
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