SOLUTION: Hi. I hope that you can help me. I have talked to others in my class, and we are all stumped with this one. Any help would be greatly appreciated. You all are awesome!!! Thanks

Question 274174: Hi. I hope that you can help me. I have talked to others in my class, and we are all stumped with this one. Any help would be greatly appreciated. You all are awesome!!! Thanks for providing this service!!
- A woman training for a duathlon trains by riding her bike or running everyday. On Monday, she runs six miles and on Tues. she rides 22.5 miles in the same amount of time she spent running on Mon. She rides 9.6 mi/hr faster than she runs. In what time should she expect to complete the duathlon if it consists of a 5 mile run, 20 mile bike ride, and a 5 mile run?
I know d=rt. I have 9.6m/hr + B= 22.5 which is 12.9 /hr times 5 would be 64.5 times two. Am I on the right track? Then, would I use R =B= 30miles? R=run and B=bikes?
Thanks you so much for your time!!! rl
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
training time first

(6 / t) + 9.6 = 22.5 / t

multiplying by t ___ 6 + 9.6 t = 22.5 ___ 9.6 t = 16.5 ___ t = 16.5 / 9.6 = 5.5 / 3.2

running speed = 6 / (5.5 / 3.2) = 19.2 / 5.5

biking speed = 22.5 / (5.5 / 3.2) = 144 / 11

D-run time = 10 / (19.2 / 5.5) = (55 / 19.2) 60 = 171.875 min = 2:51:37.5 (2 hr 51 min 37.5 sec)

D-bike time = 20 / (144 / 11) = (220 / 144) 60 = 91 2/3 min = 1:31:40 (1 hr 31 min 40 sec)

duathlon time ___ 4:23:17.5
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