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Working together, Shawn and Hector can install a tile floor in 6 hours. It would take Shawn 9 hours to do the job alone.

What is the value of r, Hector’s rate of work in part per hour?

User Vihung
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Answer: Let's assume Hector's rate of work (r) is measured in parts per hour. Since we know that Shawn and Hector together can install the tile floor in 6 hours, we can set up an equation based on their rates of work.

Shawn's rate of work (s) is 1 job in 9 hours, so his rate is:

s = 1 job / 9 hours

Hector's rate of work (r) is the unknown we want to find.

Together, their combined rate of work (s + r) is 1 job in 6 hours:

s + r = 1 job / 6 hours

Now, we can solve for Hector's rate (r):

r = 1 job / 6 hours - s

Substitute the value of s:

r = 1 job / 6 hours - 1 job / 9 hours

To find a common denominator, which is 18, let's rewrite the fractions:

r = (3/18) - (2/18)

r = 1/18

So, Hector's rate of work (r) is 1 part per hour (or 1/18 job per hour).

User Estmatic
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