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Julli [10]
2 years ago
15

Randy and trey take turns cleaning offices on the weekends. it takes randy at most 4 hours to clean the offices. it takes trey a

t most 6 hours to clean the offices. what is the greatest amount of time it would take them to clean the offices together?
Mathematics
1 answer:
Harman [31]2 years ago
4 0

Answer:

2.4 hours

Step-by-step explanation:

Because 1 hour Randy clean 1/4 of the room and Trey is 1/6. So we add both together and get that they clean 5/12 of the office in one hour. So 2.4 hours is the greatest amount of time it would take them to clean offices together

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larisa86 [58]

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Let, AC = 3x and CM = 4x.

In the right-angled triangle ACM, we have

AM^2=AC^2+CM^2=(3x)^2+(4x)^2=9x^2+16x^2=25x^2\\\\\Rightarrow AM=5x.

Now,

AM=AP+PM=AP+(AP+1)\\\\\Rightarrow 2AP=AM-1\\\\\Rightarrow 2AP=5x-1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(A)

Now, since CP ⊥ AM, so ΔACP and ΔMCP are both right-angled triangles.

So,

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Comparing equations (A) and (B), we have

5x-1=7x^2-1\\\\\Rightarrow 5x=7x^2\\\\\Rightarrow x=\dfrac{5}{7},~\textup{since }x\neq 0.

Thus,

AM=5\times\dfrac{5}{7}=\dfrac{25}{7}=3\dfrac{4}{7}.

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Step-by-step explanation:

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