To determine the time when cyclist B overtakes cyclist A, we need to calculate the time it takes for B to catch up to A. Let's set up the equation to solve for the time.
Let t be the time (in hours) it takes for cyclist B to overtake cyclist A. Since cyclist A started 30 minutes earlier than cyclist B, the time for cyclist A is t + 0.5 hours.
The distance covered by cyclist A is given by: Distance A = Speed A × Time A Distance A = 8 km/h × (t + 0.5 h)
The distance covered by cyclist B is given by: Distance B = Speed B × Time B Distance B = 10 km/h × t
Since cyclist B overtakes cyclist A, the distances covered by both cyclists are the same. Therefore, we can set up the equation:
8 km/h × (t + 0.5 h) = 10 km/h × t
Let's solve for t:
8t + 4 = 10t
4 = 2t
t = 2 hours
So, cyclist B overtakes cyclist A after 2 hours.
To find the time when B overtakes A, we add 2 hours to the starting time of cyclist B:
7:30 AM + 2 hours = 9:30 AM
Cyclist B overtakes cyclist A at 9:30 AM.