Question

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

Answer 1

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