Answer: 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
