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Suzette ran and biked for a total of 44.75 mi in 4 h. Her average running speed was 6.5 mph and
her average biking speed was 14 mph.
Let x = total hours Suzette ran. Let y = total hours Suzette biked.
a) Write the system of two equations you’ll need to solve this problem. (2 points)
b) Use substitution OR linear combination to solve for x and y. Show ALL of your work.
(4 points)
How many hours did Suzette run? ________ How many hours did she bike? _________
c) Check your work by using substitution.

Respuesta :

oladayoademosu

a. Write the system of two equations

The required system of equations to solve the problem is

6.5x + 14y = 44.75 (1)and

x + y = 4 (2)

Since Suzette ran at an average speed of 6.5 mph and ran for x hours, the total distance she ran is d = 6.5 mph × x hours = 6.5x miles.

Also, Suzette biked at an average speed of 14 mph and biked for y hours, the total distance she biked is d' = 14 mph × y hours = 14y miles.

So, the total distance she travelled is D = d + d' = 6.5x + 14y.

Also, the total time she travelled T = x + y

Since, the total distance she travelled is 44.75 miles, D = 44.75 miles.

So, 6.5x + 14y = 44.75

Also, the total time she travelled is 4 hours. So, T = 4 h

So, x + y = 4

So, the required system of equations to solve the problem is

6.5x + 14y = 44.75 (1)and

x + y = 4 (2)

b. Use substitution OR linear combination to solve for x and y

Suzette ran for 1.5 hours and Suzette biked for 2.5 hours

Solving the system of equations

6.5x + 14y = 44.75 (1)

x + y = 4 (2)

From (2), x = 4 - y

Substituting x into (1), we have

6.5x + 14y = 44.75

6.5(4 - y) + 14y = 44.75

Expanding the bracket, we have

26 - 6.5y + 14y = 44.75

collecting like terms, we have

26 + 7.5y = 44.75

Subtracting 26 from both sides, we have

7.5y = 44.75 - 26

7.5y = 18.75

dividing both sides by 7.5, we have

y = 18.75/7.5

y = 2.5 hours

Since x = 4 - y

x = 4 - 2.5

x = 1.5 hours

Since x = total hours Suzette ran and x = 1.5 hours. So, Suzette ran for 1.5 hours.

Also, y = total hours Suzette biked and y = 2.5 hours. So, Suzette biked for 2.5 hours

So, Suzette ran for 1.5 hours and Suzette biked for 2.5 hours

c. Check your work by using substitution.

Since x = 1.5 and y = 2.5 give consistent equations, x = 1.5 and y = 2.5 are the solutions of the system of equations.

Substituting x = 1.5 hours and y = 2.5 hours into the system of equations, we have

6.5x + 14y = 44.75 (1)and

x + y = 4 (2)

6.5(1.5) + 14(2.5) = 44.75 (1)and

9.75 + 35 = 44.75 = L.H.S = 44.75 = R.H.S

Also,

x + y = 1.5 + 2.5 = 4 = L.H.S = 4 = R.H.S

Since x = 1.5 and y = 2.5 give consistent equations, x = 1.5 and y = 2.5 are the solutions of the system of equations.

Learn more about system of equations here:

https://brainly.com/question/13729904

Suzette ran for 1.5 hours and biked for 2.5 hours.

a. Let x = total hours Suzette ran.

Let y = total hours Suzette biked.

The equation to solve the question will be:

x + y = 4 ....... i

6.5x + 14y = 44.75 ....... ii

b. x + y = 4 ....... i

6.5x + 14y = 44.75 ....... ii

From equation i, x = 4 - y

Put x = 4-y into equation into equation ii

6.5x + 14y = 44.75

6.5(4 - y) + 14y = 44.75

26 - 6.5y + 14y = 44.75

Collect like terms

-6.5y + 14y = 44.75 - 26

7.5y = 18.75

Therefore, y = 18.75/7.5

y = 2.5

Therefore, she bikes for 2.5 hours

Since x + y = 4

x = 4 - y

x = 4 - 2.5

x = 1.5

She ran for 1.5 hours.

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https://brainly.com/question/24578032

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