Many people enjoy challenging themselves by running in marathons. A marathon is a 26-mile race. The runners wear numbers that id
entify them so their progress can be tracked at checkpoints throughout the race. Such races can be modeled using equations. An athlete is running in a marathon that eventually finishes at a local high school. After x minutes, the distance the athlete is from the school is given by y (in miles), where x + 10y = 260 (Note: 0 ≤ x ≤ 10 and 0 ≤ y ≤ 26). Use the relationship between x and y to find the time it takes for the runner to reach the school.
<span>To x, we can use the equation x + 10y = 260. Solving for x, we now have x = 260 - 10y. We know that at the end, the runner is 0 miles from the school, so y = 0. Therefore x = 260 minutes.</span>
First we clear y from the given equation x + 10y = 260 10y = 260-x y = (260-x) / (10) Then, we evaluate the function within the domain of it x = 0 y = (260- (0)) / (10) y = (260) / (10) y = 26 x = 10 y = (260- (10)) / (10) y = (250) / (10) y = 25 That is, you travel 1 mile in 10 minutes. Therefore, traveling 26 miles will take: (26) * (10) = 260 min answer it takes for the runner to reach the school 260min.
