5. Beth can tile a floor in about 6 hours. When Beth and Mike worktogether they can tile a floor in about 2.4 hours. About how long wouldit take Mike to tile a floor if he works by himself?

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03-11-2022
Mathematics

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5. Beth can tile a floor in about 6 hours. When Beth and Mike worktogether they can tile a floor in about 2.4 hours. About how long wouldit take Mike to tile a floor if he works by himself?

Sagot :

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AmikaA376986 AmikaA376986 · Answer 1 · 2022-11-03T23:45:44-04:00

From the information given we can say that the work of rate of Beth is 6h/floor. When they work together with Mike, we can represent the situation with the equation:

[tex]\frac{t}{B}+\frac{t}{M}=1[/tex]

Where B is the rate of Beth and M is the rate of Mike, t is equal to 2.4 hours. Replacing the values we have:

[tex]\begin{gathered} \frac{2.4}{6}+\frac{2.4}{M}=1 \\ 0.4\text{ }+\frac{2.4}{M}=1\text{ (Dividing)} \\ \text{ }\frac{2.4}{M}=1\text{ }-0.4\text{ (Transposing 0.4 to the other side of the equation)} \\ \frac{2.4}{M}=0.6(\text{ Subtracting)} \\ \frac{2.4}{0.6}=M\text{ (Isolating M)} \\ 4\text{ =M} \\ \text{Answer is: Mike takes 4 hours to tile a floor} \end{gathered}[/tex]

Sagot :

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