Suppose you have entered an 85-mile biathlon that consists of a run and a bicycle race. during your run, your average velocity
is 9 miles per hour, and during your bicycle race, your average velocity is 29 miles per hour. you finish the race in 5 hours. what is the distance of the run
X= number of hours in run y = number of hours in bike race
9x+29y=85 x+y=5, and y=5-x
Substituting 5-x for y in the first equation, we have 9x+ 29(5-x)=85 and 9x+145-29x=85, then subtracting 145 from both sides to get -20x=-60 and x=3, which is the amount of hours in the running race. Multiply that by 9 miles per hour to get 27 miles
