Question

Jeanie completed a 27 mile duathlon (a race that is a combination of running and biking) in exactly 2 hours. she ran an average speed of 8.5 miles per hour and biked an average speed of 16 miles per hour. for how long did jeanie bike during the race?

Answer 1

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