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PilotLPTM [1.2K]
3 years ago
15

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, the part of the tile that hector could install in 1 hour?

Mathematics
2 answers:
Vikki [24]3 years ago
8 0
First, let x be the number of hours it will take for Hector to finish the same job alone. This means that every hour, Hector can do 1/x of the job. The amount of work done by Shawn and Hector in 6 hours should be equal to 1 complete work. This can be expressed as,
                      (1/9 + 1/x)(6) = 1
The value of x is 18. Thus, Hector can to 1/18 of the job in one hour. 
Evgen [1.6K]3 years ago
5 0

Answer:

A. 1/18

Step-by-step explanation:

Just did it!!

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Question 1 Answer:

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Question 2 Answer:

We use algebra and our previous pairings to determine the length of each task.

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<u>Centerpieces --> 7/4 hours</u>

x = time together    \frac{1}{x} = rate of completion

Mom = \frac{1}{3.5} Aunt 2 = \frac{1}{3.5}

\frac{2}{7} + \frac{2}{7}  = \frac{1}{x}

\frac{4}{7} = \frac{1}{x}

x = \frac{7}{4}

<u>Balloons --> 15/16 hours</u>

x = time together    \frac{1}{x} = rate of completion

You = \frac{1}{1.5} Grandma 2 = \frac{1}{2.5}

\frac{2}{3} + \frac{2}{5}  = \frac{1}{x}

\frac{16}{15} = \frac{1}{x}

x = \frac{15}{16}

Shortest amount of time to complete all tasks is:

\frac{6}{7} + \frac{7}{4} + \frac{15}{16} = \frac{397}{112}  ≈ 3.54 hours

Converting hours to hours and minutes --> 3 hours 32 minutes

Therefore they must arrive by 5:28pm to complete the tasks in time to leave at 9:00pm.

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