Question

Yolanda wants to complete the 50-mile biathlon in 5 hours. she gets her jogging rate up 6 miles/hour and her biking rate up to 12 miles/hour. she finishes the race in 5 hours. how many hours will she have to jog and how many hours will she have to bike to reach her goal?

Answer 1

Let x be the number of hours she jogs, and y be the number of hours she bikes.
The total time would then be x + y = 5
The total distance (based on the given speeds) would be 6x + 12y = 50
Multiply the first equation by 6 to get 6x + 6y = 30
Subtract this from the second equation to get 6y = 20
y = 10/3 or 3 1/3
Substitute this value back into the first equation to get x = 5/3 or 1 2/3
Therefore, Yolanda will have to jog 1 2/3 hours and bike 3 1/3 hours.