Let x = the miles Jeanie ran
y = the miles Jeanie biked
T = 2 hours total time for the duathlon
v1 = 8.5 mph Jeanie's running speed and
v2 = 16 mph Jeanie's biking speed
But T = Jean's time she ran t1 + time she biked t2 I. e t1 + t2 = 2
So we have average speed v2 when she biked = distance (y) / time (t2)
Distance y = v2 * t2 = 16 * t2 and distance when she ran x = 8.5 * t1
Since she covered 27 miles while running and biking we have
x + y = 27
8.5t1 + 16t2 =27 ------(1)
t1 + t2 = 2 --------------(2)
The simultaneous equation gives us
t1 = 2/3 and t2 which is time she biked = 4/3
So 4/3 = 1 1/3. Which is 1 hour 20 minutes
