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Katen [24]
3 years ago
12

Devontre rode his bike uphill 5 miles and then back downhill. The rate at which Devontre traveled downhill was 20 mph faster tha

n his rate going uphill. If it took him 20 minutes longer to ride uphill than downhill, what was his uphill rate?
Mathematics
1 answer:
Daniel [21]3 years ago
5 0

Answer:

10 mph

Step-by-step explanation:

Let x mph be Devontre rate uphill, then x+20 mph its his rate downhill.

1. Time uphill:

\dfrac{5}{x}\ hours

2. Time downhill:

\dfrac{5}{x+20}\ hours

3. If it took him 20 minutes (1/3 hour) longer to ride uphill than downhill, then

\dfrac{5}{x}-\dfrac{5}{x+20}=\dfrac{1}{3}

Solve this equation:

\dfrac{5(x+20)-5x}{x(x+20)}=\dfrac{1}{3}\\ \\\dfrac{100}{x(x+20)}=\dfrac{1}{3}\\ \\300=x(x+20)\\ \\x^2+20x-300=0\\ \\D=20^2-4\cdot (-300)=400+1200=1600\\ \\x_{1,2}=\dfrac{-20\pm \sqrt{1600}}{2}=\dfrac{-20\pm 40}{2}=-30,\ 10.

The rate cannot be negative, thus, x=10 mph (rate uphill).

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In economics, the downward sloping demand curve is used to illustrate the law of diminishing marginal utility. This means that if more of the product is consumed, the marginal benefit to the consumer falls. This is also the instance in which the consumers are willing to pay less than the original amount for the same product. 
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What the answer and how do you solve it pls
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A desk costs $44, but they boost the price 150%
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Which has the greater area: a 6 6‐centimeter by 4 1 2 412‐centimeter rectangle or a square with a side that measures 5 5 centime
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Answer:

The square with side 5 centimeters have a greater area.

Corrected question;

Which has the greater area: a 6‐centimeter by 4.12‐centimeter rectangle or a square with a side that measures 5 centimeters?

Step-by-step explanation:

The Area of a rectangle can be written as;

Area A = length × breadth

Given;

Length = 6 cm

Breadth = 4.12 cm

Substituting the values;

Area of rectangle = 6cm × 4.12cm = 24.72 cm^2

For the square;

Area of a square = length × length

Given;

Length = 5 cm

Substituting the values;

Area of the square = 5cm × 5cm = 25 cm^2

Since 25 cm^2 is greater than 24.72 cm^2

The square has a greater area.

4 0
3 years ago
Brian works 40 hours a week. He spends 40% of his time helping customers, 13% doing paperwork, and the remainder performing othe
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3 years ago
Homes in your neighborhood appreciates at a rare Of 3.5% annually. The family purchase a home in your neighborhood with a value
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Answer: it will take 13 years for the home to be valued at 250,000

Step-by-step explanation:

The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

y = b(1 + r)^ t

Where

y represents the value of the house after t years.

t represents the number of years.

b represents the initial value of the house.

r represents rate of growth.

From the information given,

b = 160000

y = 250000

r = 3.5% = 3.5/100 = 0.035

Therefore

250000 = 160000(1 + 0.035)^t

250000/160000 = (1.035)^t

1.5625 = (1.035)^t

Taking log of both sides to base 10

Log 1.5625 = log1.035^t = tlog1.035

0.1938 = t × 0.0149

t = 0.1938/0.0149

t = 13 years

8 0
3 years ago
Read 2 more answers
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