Jules is training for a marathon. She finds that for the first 5 km of her training run, she runs at a constant speed of x km/h. For the remaining 7 km of her training run, her speed reduces
by 5 km/h. Write an algebraic expression for the total time Jules takes to run 12 km. Recall that s=t/d.
you have the formula, so plug and chug. t = d/s
time: 5/x + 7/(x-5) = (12x-25)/(x^2 - 5x)
To find the total time Jules takes to run 12 km, we can break it down into two parts: the time it takes for Jules to run the first 5 km and the time it takes for her to run the remaining 7 km.
Let's start with the time it takes for Jules to run the first 5 km. We know that her speed is x km/h for this portion. The distance (d) is 5 km, and the speed (s) is x km/h. So, the time it takes (t1) can be found using the formula s = t/d:
t1 = d/s = 5/x
Next, let's consider the time it takes for Jules to run the remaining 7 km. Her speed reduces by 5 km/h for this portion, so her speed is now (x - 5) km/h. The distance is 7 km, and the speed is (x - 5) km/h. Using the same formula, we can find the time it takes (t2):
t2 = d/s = 7/(x - 5)
Finally, to find the total time it takes for Jules to run 12 km, we add t1 and t2:
Total time = t1 + t2 = 5/x + 7/(x - 5)
So, the algebraic expression for the total time Jules takes to run 12 km is 5/x + 7/(x - 5).