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Alternative formats are:

18/5 hours = 3 & 3/5 hours

18/5 hours = 3.6 hours

3.6 hours = 3 hours, 36 minutes

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.

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

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

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