Algebra 2 function question

Question

Karen Kurreck's bicycling speed is inversely proportional to the slope of the hill. If she can go up a 3 miles hill at 8% grade in 18 minutes, how long does it take her to go up a 2 mile hill at 6% grade.

Answer 1

Hi Billy,

 

Since speed is inversely proportional to the slope of the hill, we describe it mathematically as  r = k/m where r is the speed and m is the slope of the hill and k is a constant of proportionality.  Distance = rate times the time. If Karen can go 3 miles in 18 minutes, her speed or rate is r = D/t  or  r = 3 mi./18 min. or 1/6 mi./min. on a hill with a slope of 8%.Therefore   1/6 = k/.08 . Solving for k gives us k = 2/150. Now we can use r = k/.06 to find the rate of the bicycle on the 6% hill as          r = (2/150)/.06 = 2/9. Now we can use D = rt to find the time for 2 miles on a 6% hill as follows 

                      2 = (2/9) t and solve for t  to get t = 9 min.