Final answer:
The new speed required for the man to reach his destination on time can be calculated by first determining the correct travel time, inclusive of the 5 minutes he currently arrives early, and then using the distance-time relation to find the new speed.
Step-by-step explanation:
The problem presented involves finding the speed at which a man should ride to reach his destination exactly on time, given that he currently arrives 5 minutes early when riding at a speed of 50 km/h. To find this new speed, we need to calculate the time it would take to travel 50 km if he were to arrive exactly on time.
Since arriving 5 minutes early means the man is using less than the allotted time, we can first determine the correct travel time by adding those 5 minutes to the time taken at 50 km/h. Thus, if T is the on-time arrival time in hours, and he currently takes T - 5/60 hours at 50 km/h, then:
50 km / (50 km/h) = T - 5/60 hours
Solving for T gives us T = 1 hour (since 50 km at 50 km/h takes exactly 1 hour) plus the 5 minutes early he arrives, so T = 1 hour and 5 minutes, or T = 1 + 5/60 hours.
Now, as the distance remains constant at 50 km, we can find the new speed, V_new, using the formula:
V_new = distance / time = 50 km / (1 + 5/60) hours
By calculating V_new, we will obtain the speed at which the man should ride to reach his destination on time.