She spent a total of 2
hours riding her bike and jogging.
She biked for 12 miles and jogged
for 6 miles. Her rate for jogging
was 10 mph less than biking rate.
What was her rate when jogging?

her rate when jogging is 5 mph

Step-by-step explanation:

Let x represent her biking rate.

Her rate for jogging was 10 mph less than biking rate. This means that her rate for jogging is (x - 10) mph.

Time = distance/speed

She biked for 12 miles. This means that the time that she spent biking is

12/x

She jogged for 6 miles. This means that the time that she spent jogging is

6/(x - 10)

She spent a total of 2

hours riding her bike and jogging. This means that

12/x + 6/(x - 10) = 2

Multiplying through by x and (x - 10), it becomes

12(x - 10) + 6x = 2x(x - 10)

12x - 120 + 6x = 2x² - 20x

2x² - 20x - 12x - 6x + 120 = 0

2x² - 38x + 120 = 0

Dividing through by 2, it becomes

x² - 19x + 60 = 0

x² - 15x - 4x + 60 = 0

x(x - 15) - 4(x - 15) = 0

x - 4 = 0 or x - 15 = 0

x = 4 or x = 15

Her jogging rate is

15 - 10 = 5 mph

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.

9 sandwiches per hour

step-by-step explanation:

when we have a rate, we want a 1 in the denominator

27/3 = 9

27 sandwiches/ 3 hours = 9 sandwiches/hour