The woman would have to jog at a faster pace on a cool day with low humidity to achieve her target heart rate because the body cools more efficiently through sweat evaporation, requiring more effort to reach the same level of exertion compared to a humid day.
If a 30-year-old woman achieves her target heart rate by jogging at 6 mph on a hot humid day, she would likely have to jog at a faster pace on a cool day with low humidity. This is because humidity affects the evaporation rate of sweat from the skin, which is a key component of the body's natural cooling mechanism. On humid days, the concentration of water in the atmosphere is higher, which reduces the evaporation rate, making it harder to cool down. Thus, she would need to exert less effort to achieve the same heart rate. However, on a cool day with low humidity, sweating and evaporation would be more effective in cooling her body, and thus she would need to run faster to reach her target heart rate compared to a humid day.
In addition, it is relevant to note that human power output is impressive, with individuals capable of generating more than a horsepower with their leg muscles for short periods by rapidly converting blood sugar and oxygen into work output. As the woman reaches the aerobic stage of exercise, her power output decreases and she breathes rapidly to metabolize more food. On a cool day, she would have to jog faster to reach the point of aerobic exercise and achieve her target heart rate, compared to a humid day.