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mr. jones jogs the same route each day. the amount of time he jogs is inversely proportional to his jogging rate.

what option gives possible rates and times for two of his jogs?

my options are:

a. 6 mph for 1.5 hours and 5 mph for 1.25 hours
b. 5 mph for 2 hours and 4 mph for 3 hours
c. 4 mph for 2.25 hours and 6 mph for 1.5 hours
d. 4.5 mph for 3 hours and 6 mph for 4 hours

Inversely proportional:

y = constant/x, or y*x = constant. Let's see which give the *same* product:

a) 6*1.5 = 5*1.25 NO
b) 5*2 = 4*3 NO
c) 4*2.25=6*1.5  YES!!!
d) 4.5*3 = 6*4 NO

So, C)!!!

a. 6 mph for 1.5 hours and 5 mph for 1.25 hours
9 miles, 6.25 miles
b. 5 mph for 2 hours and 4 mph for 3 hours
10 miles, 12 miles
c. 4 mph for 2.25 hours and 6 mph for 1.5 hours
9 miles, 9 miles
d. 4.5 mph for 3 hours and 6 mph for 4 hours
13.5 miles, 24 miles
C.) would be the best choice here as the amount of time is inversely proportional to the jogging rate; however, the route is always the same distance. C.) is the only option where the distances are equal, and is the best choice as such.