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, so
t = 5/s + 1/(2s) + 2/(2s-12) = (13s-66)/(2s^2-12s)
To determine the time it takes for the rider to finish the race in terms of the speed "s," we can break down the different segments of the race and calculate the time taken for each segment individually.
Let's start with the flat stretch of road, which is 5 miles long. Since the rider covers this distance at a speed of "s" mi/h, we can calculate the time taken for this segment using the formula:
Time = Distance / Speed
So, for the flat stretch of road, the time taken is:
Time1 = 5 / s
Next, the rider doubles her speed down a hill that is 1 mile long. Therefore, her speed down the hill would be 2s mi/h. To calculate the time taken for this segment, we again use the formula:
Time = Distance / Speed
So, the time taken for this segment is:
Time2 = 1 / (2s)
Finally, the rider reduces her downhill speed by 12 mi/h to ride the last 2 miles of the race. Her speed for this segment would be (2s - 12) mi/h. Using the formula again, we find:
Time = Distance / Speed
So, the time taken for this segment is:
Time3 = 2 / (2s - 12)
To determine the total time taken for the race, we add up the times for each segment:
Total Time = Time1 + Time2 + Time3
= 5 / s + 1 / (2s) + 2 / (2s - 12)
Therefore, the function that gives the time "t" it takes for the rider to complete the race in terms of the speed "s" is:
t(s) = 5 / s + 1 / (2s) + 2 / (2s - 12)