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Alenkinab [10]
3 years ago
7

A turtle crawling at a rate of .1 (mi)/(h ) passess a resting bunny that rests for 30 minutes but moves 5 (mi)/(h ). How many fe

et must the bunny run to catch the turtle
Mathematics
1 answer:
antiseptic1488 [7]3 years ago
3 0

The bunny needs to run approximately 269.39 feet

<em><u>Solution:</u></em>

Let "x" be the number of hours passed since the turtle passed the buuny

Given that turtle crawls at a rate of 0.1 miles per hour

Then for "x" hours, distance traveled by turtle is 0.1x miles

Also given that bunny moves at 5 miles per hour but rests for 30 minutes

1 hour = 60 minutes

Therefore,

30 minutes = 0.5 hours

So the bunny rests for 0.5 hours

Thus the distance traveled by bunny is 5(x - 0.5) miles

To find when they will pass each, set the two distances equal to each other

0.1x = 5(x - 0.5)

0.1x = 5x - 2.5

5x - 0.1x = 2.5

4.9x = 2.5

x = 0.51

<em><u>Thus the distance ran by buuny is:</u></em>

Distance = 5(x - 0.5)

Substitute x = 0.51

Distance = 5(0.51020 - 0.5)

Distance = 5(0.010) = 0.05102 miles

Convert to feet

1 mile = 5280 feet

0.05102 miles = 0.05102 x 5280 feet = 269.39 feet

Thus the bunny needs to run approximately 269.39 feet

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n, n + 2 - two consecutive even integers

3n = 2(n + 2) + 16     |use distributive property

3n = (2)(n) + (2)(2) + 16

3n = 2n + 4 + 16

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3 years ago
Simplify the expression 2(2-x)-3x
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</span>=(2)(2)+(2)(−x)+−3x
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<span>Next is to Combine like terms..
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3 years ago
32
nata0808 [166]

Answer:

I believe it would be 4 seconds

Step-by-step explanation:

PLATO/Edmentum

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3 years ago
A clothing manufacturer uses the model a=f+4−−−−√−36−f−−−−−√ to estimate the amount of fabric to order from a mill. In the formu
Anit [1.1K]

Questions:

A clothing manufacturer uses the model a = √(f + 4) - √(36 - f) to estimate the amount of fabric to order from a mill. In the formula, a is the number of apparel items (in hundreds) and f is the number of units of fabric needed. If 400 apparel items will be manufactured , how many units of fabric should be ordered?

Answer:

32 units of fabrics

Step-by-step explanation:

Given

a = \sqrt{f + 4} - \sqrt{36 - f}

Required

Find f when a  = 4

Substitute 4 for a

4 = \sqrt{f + 4} - \sqrt{36 - f}

Rewrite as:

\sqrt{36 - f} + 4 = \sqrt{f + 4}

Square both sides

(\sqrt{36 - f} + 4)^2 = (\sqrt{f + 4})^2

(\sqrt{36 - f} + 4)^2 = f + 4

36 - f + 8\sqrt{36 - f} + 16 = f + 4

Collect Like Terms

8\sqrt{36 - f}= f +f+ 4 - 36 -16

8\sqrt{36 - f}= 2f -48

Divide through by 2

4\sqrt{36 - f}= f -24

Square both sides

16(36-f) = (f - 24)^2

16(36-f) = f^2 - 48f + 576

576-16f = f^2 - 48f + 576

-16f = f^2 - 48f

Collect like terms

f^2 - 48f + 16f = 0

f^2 -32f = 0

Factorize

f(f - 32) = 0

f = 0 or f = 32

f can not be 0 because some units must be ordered.

So, f = 32

6 0
3 years ago
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