Final answer:
To find the correct speed for the man to be on time, we need to solve for T, the time it takes to travel 50 km at the correct speed, using the provided information of being early or late with different speeds. Once T is found, we calculate the speed as 50 km divided by T.
Step-by-step explanation:
To determine the speed at which the man should ride so that he is neither late nor early, we need to calculate the correct average speed using the given information that at 50 km per hour he arrives 5 minutes early and at 40 km per hour he is 10 minutes late for a 50 km distance.
Let's denote T as the time the man should take to cover the 50 km distance without being early or late. If he travels at 50 km per hour and arrives 5 minutes early, the time taken at this speed (T_50) would be T - 5/60 hours. Since speed is distance over time, we can write:
50 km/h = 50 km / (T - 5/60) hours
Similarly, if he travels at 40 km per hour and is 10 minutes late, the time taken at this speed (T_40) would be T + 10/60 hours:
40 km/h = 50 km / (T + 10/60) hours
We then solve these two equations for T, the correct travel time. Once T is obtained, the correct speed (V) is calculated using V = 50 km / T.