<h3>Answer: 18/5 hours</h3>
Alternative formats are:
18/5 hours = 3 & 3/5 hours
18/5 hours = 3.6 hours
3.6 hours = 3 hours, 36 minutes
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Explanation:
Let,
x = time it takes for Blake to do the job alone
y = time it takes for Ned to do the job alone
z = time it takes to do the job if they work together
In this case,
x = 9, y = 6 and z is unknown which we want to solve for.
The equation to solve is
1/x + 1/y = 1/z
So,
1/x + 1/y = 1/z
1/9 + 1/6 = 1/z
18z(1/9 + 1/6) = 18z(1/z)
18z(1/9) + 18z(1/6) = 18z(1/z)
2z + 3z = 18
5z = 18
z = 18/5
It takes them 18/5 hours if they worked together.
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Here's an alternative way to look at it
Blake takes 9 hours if he works alone, so his rate is 1/9 of a room per hour. Similarly, Ned's rate is 1/6 of a room per hour. Their combined rate is
1/9 + 1/6 = 2/18 + 3/18 = 5/18
So,
(total rate)*(total time) = 1
(5/18)*z = 1
z = 1/(5/18)
z = 18/5
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Side note
18/5 = (15+3)/5
18/5 = 15/5 + 3/5
18/5 = 3 + 3/5
18/5 = 3 & 3/5
also,
18/5 = 3 + 3/5
18/5 = 3 + 0.6
18/5 = 3.6
and,
3.6 hours = 3 hours + 0.6 hours
3.6 hours = 3 hours + (0.6*60 minutes)
3.6 hours = 3 hours + 36 minutes
3.6 hours = 3 hours, 36 minutes
