On a 200 km bike cycle ride, you ride the first 90 km at an average speed of 20 m/s. What must your average speed over the next 40 km be to have your average speed for the total 200 km be?
(a) 60 m/s?
(b) Given this average speed for the first 90 km, can you possibly attain an average speed of
80 m/s for the total 200 km ride? Explain.
90*10^3 m (1 s / 20 m) = 4.5 *10^3 s
Hey, 90 + 40 = 130, not 200. Typo?
Part b
V = speed for first 90
total time = 90/V + 110/ Vfinal = 200 / 80
110/Vfinal = 2.5 - 90/V
if 90/V is greater than 2.5, you have negative time for final leg
To find out the average speed for the total 200 km bike cycle ride, we need to consider both the distance traveled and the time taken for each part of the ride.
Let's break down the problem step by step:
Step 1: Find the time taken for the first 90 km at an average speed of 20 m/s.
Time = Distance / Speed = 90 km / 20 m/s = 4500 seconds
Step 2: Find the remaining distance for the total ride.
The remaining distance is 200 km - 90 km = 110 km.
Step 3: Find the remaining time required for the total ride, assuming an average speed of 60 m/s (option a).
Time = Distance / Speed = 110 km / 60 m/s = 1833.33 seconds
Step 4: Find the time required for the remaining 40 km, assuming the same average speed as the first 90 km.
Time for 40 km = Distance / Speed = 40 km / 20 m/s = 2000 seconds
Step 5: Find the remaining time for the total ride.
Remaining time = Time required for remaining 40 km + Time required for remaining distance
Remaining time = 2000 seconds + 1833.33 seconds = 3833.33 seconds
Step 6: Find the average speed for the total 200 km bike cycle ride.
Average Speed = Total Distance / Total Time
Average Speed = 200 km / (4500 seconds + 3833.33 seconds) ≈ 200 km / 8333.33 seconds
Option (a): 60 m/s
To check if an average speed of 60 m/s is possible for the total 200 km ride, we substitute it into the calculation.
Average Speed = Total Distance / Total Time
60 m/s = 200 km / (4500 seconds + 3833.33 seconds)
After solving the equation, the time required for the total ride is approximately 222.22 seconds, which is not possible given the previous calculations.
Option (b): 80 m/s
To check if an average speed of 80 m/s is possible for the total 200 km ride, we substitute it into the calculation.
Average Speed = Total Distance / Total Time
80 m/s = 200 km / (4500 seconds + 3833.33 seconds)
After solving the equation, the time required for the total ride is approximately 166.67 seconds, which is less than the time required for the first 90 km (4500 seconds). Thus, it is not possible to attain an average speed of 80 m/s for the total 200 km ride.
Therefore, the only valid option is none of the above.