SOLUTION: suppose you have entered a 121-mile biathlon that consists of a run and bicycle race. During your run, your average velocity is 6 miles per hours, and during your bicycle race, you
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Question 880936: suppose you have entered a 121-mile biathlon that consists of a run and bicycle race. During your run, your average velocity is 6 miles per hours, and during your bicycle race, your average velocity is 23 miles per hour. You finish the race in 6 hours. What is the distance of the run? What is the distance of the bicycle race? Found 2 solutions by lwsshak3, josmiceli:Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! suppose you have entered a 121-mile biathlon that consists of a run and bicycle race. During your run, your average velocity is 6 miles per hours, and during your bicycle race, your average velocity is 23 miles per hour. You finish the race in 6 hours. What is the distance of the run? What is the distance of the bicycle race?
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let x=distance of the running race
121-x=distance of the bicycle race
travel time=distance/velocity
..
lcd=6*23=138
23x+6(121-x)=6*138
23x+726-6x=828
17x=102
x=6
121-x=115
distance of the running race = 6 miles
distance of the bicycle race=115 miles
You can put this solution on YOUR website! Let = the distance in miles for the run = the distance in miles for the bicycle race
Let = the time in hrs for the run = the time in hrs for the bicycle race
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Equation for the run:
(1)
Equation for the bicycle race:
(2)
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(2)
(2)
(2)
(2)
Substitute (1) into (2)
(2)
(2)
(2)
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Substitute this result back into (1)
(1)
(1)
(1)
and
The bicycle race is 115 mi
check:
(2)
(2)
(2)
(2)
OK
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