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4vir4ik [10]
3 years ago
13

If Alex and Brandon work together they will clean the school in 15 hours. Working alone, Brandon can finish the same job in 20 h

ours. How long will it take Alex to do the job by himself? PLEASE HELP ME PRETTY PLEASE
Mathematics
1 answer:
sesenic [268]3 years ago
8 0

Answer:

It takes 60 hours for Alex to complete the job alone.

Step-by-step explanation:

Given:

Number of hours Brandon alone can finish job =20 hours

Let the number of hours required by Alex alone to complete the job be 'x' hrs.

We need to find the number of hours required by Alex alone to complete the job.

Solution:

Now we can say that;

Rate at which Alex can complete the job alone = \frac1x job/hour

Rate at which Brandon can complete the job alone = \frac{1}{20} job /hour

Also Given:

Number of hours required for both to complete the job = 15

So rate of both complete the job  = \frac{1}{15} job/hour

Now we can say that;

rate of both complete the job is equal to sum of Rate at which Alex can complete the job alone and Rate at which Brandon can complete the job alone.

framing in equation form we get;

\frac1x+\frac{1}{20}=\frac{1}{15}

Now taking LCM for making the denominators same we get;

\frac{20}{20x}+\frac{x}{20x}=\frac{1}{15}

Now denominators are common so we will solve the numerators.

\frac{20+x}{20x}=\frac{1}{15}

Now Using cross multiplication we get;

15(20+x)=20x

Applying Distributive property we get;

15\times20+15\times x =20x\\\\300+15x=20x

Combining like terms we get;

300=20x-15x\\\\300=5x

Now Dividing both side by 5 we get;

\frac{300}{5}=\frac{5x}{5}\\\\x=60\ hrs

Hence It takes 60 hours for Alex to complete the job alone.

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3 years ago
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Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 73 and 9
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Answer: After about 9.03 hours the temperature first reach 82 degrees.

Step-by-step explanation:

The sinusoidal function is given by :

y=A\sin[\omega(x-\alpha)]+C

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As per given,

Average daily temperature= C=\dfrac{73+97}{2}=85   [midline is average of upper and lower limit.]

A=  97-85 = 12

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\omega=\dfrac{2\pi}{24}=\dfrac{\pi}{12}

Substitute all values in sinusoidal function, we get

y=12\sin[\dfrac{\pi}{12}(x-10)]+85

Put y= 82, we get

82=12\sin[\dfrac{\pi}{12}(x-10)]+85\\\\\Rightarrow\ -3= 12\sin[\dfrac{\pi}{12}(x-10)]\\\\=\dfrac{-1}{4}= \sin[\dfrac{\pi}{12}(x-10)]\\\\\Rightarrow\ \dfrac{\pi}{12}(x-10)=\sin^{-1}(\dfrac{-1}{4})\\\\\Rightarrow\ x-10=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))\\\\\Rightarrow\ x=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))+10\\\Rightarrow\ x\approx9.03

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3 years ago
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6 0
3 years ago
An engineer is designing a fountain that shoots out drops of water. The nozzle from which the water is launched is 3 meters abov
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Answer:

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Step-by-step explanation:

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Required

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When the drop hits the ground,

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So, we have:

0 = -5t^2 + 14t + 3

Rewrite as:

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Factorize

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Factor out 5t + 1

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Split

t -3 = 0 or 5t + 1 = 0

Solve for t

t = 3 or 5t = -1

Time cannot be negative.

So:

t = 3

5 0
3 years ago
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