In a bike race, a rider covers a 5 mi flat stretch of road at a speed of s mi/h. She then doubles her speed down a hill 1 mi long. Finally, she reduces her downhill speed bu 12 mi/h as she rides the last 2 mi of the race. What function gives the time t it takes the rider finish the race in terms of s?

time=distance/speed=5/s+1/2s + 2/(2s-12)

To find the function that gives the time it takes for the rider to finish the race in terms of s, we need to calculate the time it takes for each segment of the race and then sum them up.

Let's break down the race into three segments:

Segment 1: The 5 mi flat stretch of road.
To calculate the time for this segment, we use the formula time = distance / speed.
So, the time for this segment is 5 / s.

Segment 2: The downhill stretch of road.
The rider doubles her speed down the hill, so her speed becomes 2s mi/h.
The distance for this segment is 1 mi.
Therefore, the time for this segment is 1 / (2s).

Segment 3: The last 2 mi of the race.
The rider reduces her downhill speed by 12 mi/h, so her speed becomes (2s - 12) mi/h.
The distance for this segment is 2 mi.
Therefore, the time for this segment is 2 / (2s - 12).

Now, let's add up the times for each segment to get the total time t:

t = Segment 1 time + Segment 2 time + Segment 3 time
= 5/s + 1/(2s) + 2/(2s - 12)

So, the function that gives the time it takes the rider to finish the race in terms of s is t = 5/s + 1/(2s) + 2/(2s - 12).