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Jean runs 10 mi and then rides 21mi on her bicycle in a biathlon. She rides 6mph faster than she runs. If the total time for her to complete the race is 2.75hr , determines her speed running and her speed riding her bicycle.

User Goma
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2 Answers

20 votes
20 votes

Answer:

i took the test its A

Explanation:

User Ipengineer
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29 votes
29 votes

Answer/Step-by-step explanation:

Speed is the distance over time.

Let x = the time riding bike

Let y = the time running

We know that the difference between the bike speed and running speed is 6 mph. We also know that the total time is 2.75 hr. Knowing these facts, we can set equations.

x + y = 2.75 eq1

(21 / x) - (10 / y) = 6 eq2

After substituting eq1 into eq2, we get

(21 / x) - (10 / (2.75 - x)) = 6

We have a rational equation with different denominators, so we need to use the LCD. LCD is x(2.75 - x).

[21(2.75 - x) - 10x] / (x(2.75 - x)) = [6x(2.75 - x)] / (x(2.75- x))

Equate numerators to solve for x.

21(2.75 - x) - 10x = 6x(2.75 - x)

57.75- 31x = 16.5x-6x^2

Add 6x^2 and subtract 16.5x^2 on both sides of the equation.

6x^2- 16.5x+57.75=0

We now have a quadratic equation. Factor out a 2.

2(3x^2-8.25+28.875)=0

Set the term in parenthesis equal to zero.

(3x^2-8.25+28.875)=0

Use the quadratic formula to solve for x:

x = (-b ± √(b^2 - 3ac)) / 2a

where:

a = 3

b = 8.25

c = 28.875

Plug in these values into the formula. You will have two solutions because of the plus/minus sign. Keep in mind that both

x ≤ 0

x = 2.75

cannot be solutions, since zero cannot be in the denominator of the original equation, and time is always positive.

Once you have your x value, plug it into

21 / x and 8 / (2.75- x)

to get the running speed and bike speed.

User SonDang
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