Final answer:
To find the lady's jogging speed, we use the relationship between distance, rate, and time, and the information that her jogging speed is 10 mph less than her biking speed. After setting up and solving the equations, we determine that her jogging speed is 7 mph.
Step-by-step explanation:
To solve the problem, we need to set up a system of equations that represent the given information. The lady spent a total of 4 hours biking and jogging. Let x represent the biking speed and y represent the jogging speed. We are told that the jogging speed is 10 mph less than the biking speed, which gives us the relationship between the two speeds: y = x - 10.
Next, we use the relationship that distance equals rate multiplied by time (d = rt). This leads to two more equations based on the distances and times for biking and jogging:
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- Biking: 14 miles = x * biking time
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- Jogging: 12 miles = y * jogging time
Since the total time spent on both activities is 4 hours, we have: biking time + jogging time = 4 hours. We can express biking time as 14/x and jogging time as 12/y. Therefore:
14/x + 12/y = 4
Substituting y = x - 10 into this equation leads to:
14/x + 12/(x - 10) = 4
This equation can be solved for x, which represents the biking speed. Once we find x, we can easily find y, the jogging speed, by subtracting 10 from x.
After solving the equation, we find that the jogging speed (y) is 7 mph, which corresponds to option B among the provided choices. Therefore, the lady's rate while jogging was 7 mph.