Complete Question:
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
If Suzette ran and biked for a total of 44.75 mi in 4 h and her average running speed was 6.5 mph with average biking speed at 14 mph and average running speed at 6.5 mph, then she must have run 1.5hours and biked for 2.5 hours
Let x = total hours Suzette ran.
Let y = total hours Suzette biked
If the total hours biked is 4 hours, then:
x + y = 4 ....... 1
Also if her average running speed was 6.5 mph and her average biking speed was 14 mph with a total of 44.75 mi in 4 hours
6.5x + 14y = 44.75 ........ 2
From equation 1,
x = 4 - y ....... 3
Substitute the value of x into the equation 2 to have:
6.5x + 14y = 44.75
6.5(4 - y) + 14y = 44.75
26 - 6.5y + 14y = 44.75
-6.5y + 14y = 44.75 - 26
7.5y = 18.75
Divide both sides by 7.5
7.5y/7.5 = 18.75/7.5
y = 2.5
This shows that Suzette biked 2.5hours
Substitute y = 2.5 into equation 1:
x + 2.5 = 4
x = 4 - 2.5
x = 1.5
This shows that Suzette ran for 1.5 hours
Hence if the average running speed was 6.5 mph and her average biking speed was 14 mph then she must have run 1.5hours and biked for 2.5 hours
Learn more here: brainly.com/question/24515212
