Final answer:
To solve this motion problem, we calculate the time taken to travel each way and the total time including the stop in Lagos. We then calculate the average speed for the entire journey. With the given information, we cannot determine the correct arrival time or average speed from the options provided.
Step-by-step explanation:
The problem described is a classic motion problem in mathematics that can be solved by using the formula for average speed, which is total distance traveled divided by total time taken. First, let's calculate the time taken for the motorist to travel from Ibadan to Lagos and back to Ibadan.
Time from Ibadan to Lagos:
142 km ÷ 60 km/h = 2.37 hours or 2 hours and 22 minutes.
Time from Lagos to Ibadan:
142 km ÷ 80 km/h = 1.775 hours or 1 hour and 47 minutes.
The motorist spent 2.5 hours in Lagos. Adding all these times gives us the total time spent on the journey:
2.37 hours + 2.5 hours + 1.775 hours = 6.645 hours.
If the motorist left at a certain time, we add the total time to this departure time to find the arrival time back in Ibadan. However, we are not given the departure time, so we cannot calculate the actual arrival time. We will need more information to determine the exact arrival time in Ibadan.
Now, let's calculate the average speed for the entire journey. The total distance traveled is twice the distance from Ibadan to Lagos because the motorist returned, so that's 142 km each way or a total of 284 km.
Average speed:
284 km ÷ 6.645 hours = approximately 42.75 km/h.
Without the specific departure time, we cannot determine the correct arrival time and none of the options for average speed match our calculation; therefore, based on the information given, we cannot select any of the options provided. This problem may contain an error or is missing information.