Answer:
option 3
Explanation:
The relationship between the time he jogs and his jogging rate is that they are inversely proportional. This means that as his jogging rate increases, the time he takes to complete the route decreases, and vice versa.
To check which of the given options is possible, we can use the formula for inverse variation:
t1 * r1 = t2 * r2
where t1 and r1 are the time and rate for one jog, and t2 and r2 are the time and rate for another jog. Let's check the options one by one:
Option 1: 4 mph for 3 hours and 6 mph for 4.5 hours
Jog 1: t1 = 3, r1 = 4
Jog 2: t2 = 4.5, r2 = 6
t1 * r1 = 3 * 4 = 12
t2 * r2 = 4.5 * 6 = 27
The equation is not satisfied, so this option is not possible.
Option 2: 3 mph for 2 hours and 4.5 mph for 3 hours
Jog 1: t1 = 2, r1 = 3
Jog 2: t2 = 3, r2 = 4.5
t1 * r1 = 2 * 3 = 6
t2 * r2 = 3 * 4.5 = 13.5
The equation is not satisfied, so this option is not possible.
Option 3: 4 mph for 3 hours and 6 mph for 2 hours
Jog 1: t1 = 3, r1 = 4
Jog 2: t2 = 2, r2 = 6
t1 * r1 = 3 * 4 = 12
t2 * r2 = 2 * 6 = 12
The equation is satisfied, so this option is possible.
Option 4: 4 mph for 2 hours and 3 mph for 3 hours
Jog 1: t1 = 2, r1 = 4
Jog 2: t2 = 3, r2 = 3
t1 * r1 = 2 * 4 = 8
t2 * r2 = 3 * 3 = 9
The equation is not satisfied, so this option is not possible.
Therefore, the option that gives possible rates and times for two of his jogs is:
4 mph for 3 hours and 6 mph for 2 hours.