1. 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)

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topeadeniran2 topeadeniran2 · Answer 1 · 2021-09-15T15:58:38+02:00

Suzette ran for 1.6 hours and biked for 2.4 hours.

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

From i, y = 4 - x

Put the value of y into equation ii

6.5x + 14y = 44.75

6.5x + 14(4 - x) = 44.75

6.5x + 56 - 14x = 44.75

Collect like terms

6.5x - 14x = 44.75 - 56

-7.5x = -11.25

x = 11.25/7.5

x = 1.6 hours

Since x + y = 4

1.6 + y = 4

y = 4 - 1.6

y = 2.4 hours.

Suzette ran for 1.6 hours and biked for 2.4 hours.

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