Final answer:
The truck should have traveled at a speed of · s = p * (p/(p-3)) · miles per hour to arrive on time, provided that p is not equal to 3. Otherwise, the truck cannot arrive on time.
Step-by-step explanation:
The question asks how fast the truck should have traveled to arrive on time, given it traveled t miles at p miles per hour but arrived 3 hours late.
To solve this, first, we need to find the time it should have taken to travel t miles. This time is the total distance divided by the speed, so t/p hours. Since the truck arrived 3 hours late, the actual travel time was t/p + 3. Now, to arrive on time, the truck should have taken t/p hours.
We need to find the required speed to cover the same distance t miles in t/p hours. Let's call this speed s. The formula then is s = t / (t/p). Simplifying this, we get s = p * (p/(p-3)) if p is not equal to 3, otherwise, the truck cannot arrive on time. Hence, the truck should have traveled at this new speed s to arrive on time.