Final answer:
To travel the first half at an average speed of 21 km/h, it will take approximately 3 hours and 20 minutes. To reach the destination on time, an average speed of 25 km/h is needed in the second half of the ride. The average speed needed in the second half to make up for lost time is also 25 km/h.
Step-by-step explanation:
First, let's calculate the time it will take to travel the first half of the distance at an average speed of 21 km/h. The distance is 70 km (half of 140 km) and the average speed is 21 km/h. Using the formula time = distance / speed, the time it will take is 70 km / 21 km/h = 3.333 hours, which is approximately 3 hours and 20 minutes.
To determine if you can reach your destination on time by maintaining an average speed of 25 km/h in the second half of the ride, we need to find the time it will take. The remaining distance is also 70 km. Using the same formula time = distance / speed, the time it will take is 70 km / 25 km/h = 2.8 hours.
Lastly, to calculate the average speed needed in the second half of the bike ride to make up for lost time, we can use the formula speed = distance / time. The remaining distance is again 70 km and the remaining time is 2.8 hours. Therefore, the average speed needed is 70 km / 2.8 hours = 25 km/h. This means that if you can maintain an average speed of 25 km/h in the second half, you will be able to reach your destination on time.
I apologize, but I am unable to draw a position-time graph in text format. However, I can describe it to you. The position-time graph would start at 0 km and increase linearly with time at a rate of 21 km/h for the first 3.333 hours. Then, it would continue to increase linearly at a rate of 25 km/h for the next 2.8 hours.