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leonid [27]
3 years ago
11

Working alone, Ryan can dig a 10 ft by 10 ft hole in 5 hours Castel can dig the same hole in 6 hours how long would it take them

if they worked together
Mathematics
1 answer:
Fed [463]3 years ago
6 0

Answer:

The time taken by both boys to complete work = 2.73 hours

Step-by-step explanation:

Time taken by rayan to dig hole  T_{1} = 5 hours

Time taken by castel to dig hole T_{2} = 6 hours

Now the time taken by both persons working together  

T = \frac{T_{1} T_{2}  }{T_{1} + T_{2}}

Put all the values in above formula we get

T = \frac{ 30 }{6 + 5}

T = \frac{30}{11}

T = 2.73 hours

Therefore the time taken by both boys to complete work = 2.73 hours

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Adam is building a computer desk with a separate compartment for the computer. The compartment for the computer is a rectangular
Alik [6]

Answer:

The width of the computer compartment is 9 inches

The length of the computer compartment is 33 inches

The height of the computer compartment is 27 inches

Step-by-step explanation:

The given data on the rectangular prism compartment are;

The volume of the rectangular prism, V = 8019 cubic inches

The length of the compartment, l = 24 inches + The width, w

The height of the compartment, h = 18 inches + The width, w

Therefore, we have;

l = 24 + w

h = 18 + w

V = l × h × w

∴ V = (24 + w) × (18 + w) × w = w³ + 42·w² + 432·w = 8019

w³ + 42·w² + 432·w - 8019 = 0

By graphing the above function with MS Excel, we have one of the solution is w = 9

∴ (w - 9) is a factor of w³ + 42·w² + 432·w - 8019 = 0

Dividing, we get;

w² + 51·w + 891

w³ + 42·w² + 432·w - 8019 = 0

w³ - 9·w²

     51·w² - 459·w

                 891·w

                 891·w + 8019

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Therefore,

w³ + 42·w² + 432·w - 8019 = 0

w³ + 42·w² + 432·w - 8019  = (x - 9)·(w² + 51·w + 891) = 0

The determinant of the factor, w² + 51·w + 891 = 51² - 4×1×891 = -963, therefore, the it has complex roots

Therefore, the real solution of (x - 9)·(w² + 51·w + 891) = 0 is w = 9

The width of the computer compartment, w = 9 inches

The length of the computer compartment, l = 24 inches + 9 inches = 33 inches

The height of the computer compartment, h = 18 inches + 9 inches = 27 inches.

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