1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
slavikrds [6]
2 years ago
10

Now let’s generalize. a. Running uphill the jogger runs c mph slower than 6 mph. Write an expression representing a speed of c m

ph slower than 6 mph. ___________
b. Write an algebraic expression that represents the time it takes to run 1 mile uphill at a speed that is c mph slower than 6 mph. ___________ (Refer to #1a for help.)
c. Running downhill the jogger runs c mph faster than 6 mph. Write an expression represents a speed of c mph faster than 6 mph. ___________
d. Write an algebraic expression that represents the time it takes to run 1 mile downhill at a speed that is c mph faster than 6 mph. ___________ (Refer to #1b for help.)
e. Use your answers to b and d to write an algebraic expression for the total time, in hours, that it takes the jogger to cover 2 miles by going uphill for 1 mile and then returning 1 mile back down the hill.
f. Simplify your answer to part e into a single algebraic fraction. (Remember to find a common denominator first.)
g. What is the value of c for #1? (How much slower does she run uphill?) ________ Use this c to test your answer to part f. (Check that it gives the correct answer for #1c.)
h. What is the value of c for #2? (How much slower does she run uphill? ) ________ Use this c to test your answer to part f. (Check that it gives the correct answer for #2.)
Mathematics
1 answer:
Vsevolod [243]2 years ago
7 0

the complete answer in the attached file (response greater than 5000 characters))

the complete question below with their respective answers

For reasonable distances, a certain jogger can maintain an average speed of 6 miles per hour while running on level ground. The jogger decides to go to a local park and use one of the paths there for a workout routine one day each week. This path is a gently sloping one that winds its way to the top of a hill.

1. The jogger can run at an average speed of 5.5 miles per hour up the slope and 6.5 miles per hour going down the slope. The jogger decides to cover 2 miles by going uphill for 1 mile and then returning 1 mile back down the hill.

a. How long does it take the jogger to run 1 mile uphill?

Let

r-------> average speed

d------ > distance in miles

t---- > is the time in hours


we know that

r=d/t-------- > t=d/r

for r=5.5 mph and d=1 mile

t=1/5.5 hours

the answer Part 1a) is (1/5.5) hours

b. How long does it take the jogger to run 1 mile downhill?

we know that

r=d/t-------- > t=d/r

for r=6.5 mph and d=1 mile

t=1/6.5 hours

the answer Part 1b) is (1/6.5) hours

c. Use your answers to a and b to determine how long, in hours, the full trip will take (1 mile uphill and 1 mile downhill). Give an exact answer expressed as a fraction in simplest terms and then give a decimal approximation correct to three decimal places.

Reduced Fraction: _________ Decimal Approximation: _________

(1/5.5)+(1/6.5)=(6.5+5.5)/(5.5*6.5)=12/35.75------ >multiply by 100 both members 1200/3575

Divide by 25 both members

48/143=0.336 hours

The answer part 1c) is

Reduced Fraction: 48/143 hours

Decimal Approximation: 0.336 hours

2. On a steeper slope, the jogger can run at an average speed of 5.3 miles per hour up the slope and 6.7 miles per hour going down the slope.

a. What is the jogger’s uphill time in hours?


Let

r-------> average speed

d------ > distance in miles

t---- > is the time in hours


we know that

r=d/t-------- > t=d/r

for r=5.3 mph and d=1 mile

t=1/5.3 hours

the answer Part 2a) is (1/5.3) hours

b. What is the jogger’s downhill time in hours?


Let

r-------> average speed

d------ > distance in miles

t---- > is the time in hours


we know that

r=d/t-------- > t=d/r

for r=6.7 mph and d=1 mile

t=1/6.7 hours

the answer Part 2b) is (1/6.7) hours

c. Use your answers to a and b to determine how long, in hours, the full trip will take (1 mile uphill and 1 mile downhill). Give an exact answer expressed as a fraction in simplest terms and then give a decimal approximation correct to three decimal places.

Reduced Fraction: Decimal Approximation:

(1/5.3)+(1/6.7)=(6.7+5.3)/(5.3*6.7)=12/35.51------ >multiply by 100 both members 1200/3551=0.338 hours

The answer part 2c) is

Reduced Fraction: 1200/3551 hours

Decimal Approximation: 0.338 hours

3. Now let’s generalize.

a. Running uphill the jogger runs c mph slower than 6 mph. Write an

expression representing a speed of c mph slower than 6 mph.


we know that

r=(6-c) mph

the answer Part 3a) is r=(6-c) mph

b. Write an algebraic expression that represents the time it takes to

run 1 mile uphill at a speed that is c mph slower than 6 mph.


we know that

r=d/t-------- > t=d/r

for r=(6-c) mph and d=1 mile

t=1/(6-c) hours

the answer Part 3b) is t=1/(6-c) hours

c. Running downhill the jogger runs c mph faster than 6 mph. Write an

expression represents a speed of c mph faster than 6 mph.


we know that

r=(6+c) mph

the answer Part 3c) is r=(6+c) mph

d. Write an algebraic expression that represents the time it takes to

run 1 mile downhill at a speed that is c mph faster than 6 mph.


we know that

r=d/t-------- > t=d/r

for r=(6+c) mph and d=1 mile

t=1/(6+c) hours

the answer Part 3d) is t=1/(6+c) hours

e. Use your answers to b and d to write an algebraic expression for the total time, in hours, that it takes the jogger to cover 2 miles by going uphill for 1 mile and then returning 1 mile back down the hill.

(1/(6-c))+(1/(6+c))

The answer part 3e) is (1/(6-c))+(1/(6+c))

f. Simplify your answer to part e into a single algebraic fraction. (Remember to find a common denominator first.)

(1/(6-c))+(1/(6+c))=((6+c)+(6-c))/(6*6-c*c)=12/(36-c^2)

The answer part 3f) is 12/(36-c^2) hours

g. What is the value of c for #1? (How much slower does she run uphill?) ________

Use this c to test your answer to part f. (Check that it gives the correct answer for #1c.)


we know that

(6-c)=5.5

c=6-5.5

c=0.5 mph

substitute the value of c in [12/(36-c^2) ]

12/(36-c^2)

12/(36-0.5^2)

12/(36-0.25)

12/35.75=48/143 hours ---- > is correct

h. What is the value of c for #2? (How much slower does she run uphill? ) ________

Use this c to test your answer to part f. (Check that it gives the correct answer for #2.)

we know that

(6-c)=5.3

c=6-5.3

c=0.7 mph

substitute the value of c in [12/(36-c^2) ]

12/(36-c^2)

12/(36-0.7^2)

12/(36-0.49)

12/35.51=1200/3551 hours ---- > is correct



Download docx
You might be interested in
Solve x^2+ 8x- 6=0 using the Quadratic Formula
CaHeK987 [17]

Answer:

x=−4+√22 or x=−4−√22

Step-by-step explanation:

Substitute all values in the quadratic formula.

Solve.

6 0
2 years ago
Read 2 more answers
What’s the solution of 2 plus 2
egoroff_w [7]

Answer: 4

Step-by-step explanation: 2 + 2 = 4

8 0
3 years ago
Read 2 more answers
What does a radius of a sphere join?
Reika [66]
<span>The radius of a sphere join refers to the (D) the center and a point on the sphere. A radius is the distance of the center point to any sides of the circle or sphere. The point on the sphere can be anywhere. The center and a point on the sphere forms a sphere join.</span>
8 0
3 years ago
1. Two or more linear inequalities in the same variable x and y are called
Serjik [45]

Step-by-step explanation:

  1. A. linear equation
  2. D. None of the above
  3. B. Boundary line Broken line
  4. A solid line
  5. 6.sorry

3 0
2 years ago
What is the volume of corn held in this cone-shaped grain silo? Use 3.14 for π and round to the nearest cubic foot. Enter your a
babymother [125]

Answer:

V = 301 ft^3

Step-by-step explanation:

The volume of a cone is given by

V =1/3 pi r^2 h

We know pi = 3.14 r =6 and

We need to determine h

We can find h from the Pythagorean theorem where 6 is a leg and 10 is the hypotenuse

h^2 +6^2 = 10^2

h^2 +36 = 100

h^2 = 64

Taking the square root of each side

h = 8

V =1/3 pi r^2 h

V = 1/3 (3.14) (6)^2 * 8

V = 301.44 ft^3

Rounding to the nearest cubic foot

V = 301 ft^3

7 0
3 years ago
Read 2 more answers
Other questions:
  • Write a word phrase for -5(x - 7)
    13·1 answer
  • Hey can you guys help me please help
    15·1 answer
  • Which of the following expressions is equal to sin(-150°)?sin(309)
    11·1 answer
  • What is the midpoint of BC
    12·1 answer
  • To make an orange drink John uses 4 cups of water and 5 spoonfuls of powder. Joan
    6·1 answer
  • Hellllpppp pleaseee??
    11·2 answers
  • Xander goes to the movies with his soccer team. Each team member buys a ticket and two
    13·1 answer
  • Help me solve this conversions problem
    5·2 answers
  • Solve |x| – 17 = 60<br> What is the correct answer
    12·2 answers
  • There is the option of buying two different rabbit colonies.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!