An athlete ran for 8 hours at a constant speed The athlete w

An athlete ran for 8 hours at a constant speed. The athlete was immediately given a bike and rode in the opposite direction for 3 hours, with twice the speed. The athlete then reversed direction again, walking for 1 hour at 40% of initial running speed. After 12 hours, the athlete was 9.6 miles from the point where the marathon exercise excursion began. Find the athlete

Solution

Running DATA:
distance= 8x miles; rate= x mph; time= 8 hrs
Biking DATA:
distance=(2x)(3 hr)=6x miles ;rate= 2x mph; time= 3 hrs
distance=0.40x ; rate=0.40x; time= 1 hour
EQUATION:
run dist. - bike distance + run dist. = 9.6 mi
8x - 6x + 0.40x = 9.6
2.4x = 9.6
x= 4 mph (running rate)
2x=8 mph (biking rate)
0.4x=1.6 mph (walking rate)