Duane rode his bike at 14 miles per hour for 3 hours, then put the bike down and began walking at miles 2 per hour. Elizabeth started jogging at 6 miles per hour along the same path at the same time that Duane started biking. When she reached the bike, she began riding it at 12 miles per hour. How many hours will it have been since they started when Elizabeth catches up to Duane?
In 3 hours D rides 14 m/h x 3 hr = 42 miles at the same time Elizabeth covers 18 miles running
D ditches his bike Elizabeth still has to run 24 miles to the bike which will take her 4 more hours at 6m/hr
in that 4 hours D covers 8 miles walking Elizabeth starts riding 12 m/hr which is 10 m/r faster than D is walking
she will close that 8 miles in 8/10 of an hour and catch D
3 hours + 4 hours + 8/10 hr = 7 4/5 hours after they started