1. Calculate the total planned time for the journey: Total Distance (60 km) / Planned Average Speed (20 km/h) = 3 hours. 2. Calculate the distance of the first half of the journey: 60 km / 2 = 30 km. 3. Calculate the actual time taken for the first half: Distance (30 km) / Actual Speed (15 km/h) = 2 hours. 4. Calculate the remaining time available to meet the original total time: Total Planned Time (3 hours) - Time Taken for First Half (2 hours) = 1 hour. 5. Calculate the distance of the second half of the journey: 60 km - 30 km = 30 km. 6. Calculate the required average speed for the second half to meet the remaining time: Distance (30 km) / Remaining Time (1 hour) = 30 km/h. 7. Compare this required speed (30 km/h) with the initial planned average speed for the second half (which, assuming constant speed throughout, would be 20 km/h). 8. Since 30 km/h is greater than 20 km/h, the cyclist must increase their average speed for the second half of the journey. Why others are wrong: A — Maintaining the initial planned speed (20 km/h) would result in the second half taking 30km / 20km/h = 1.5 hours, making the total journey time 2 + 1.5 = 3.5 hours, which exceeds the planned 3 hours. B — Decreasing the speed would further increase the time taken for the second half, making it impossible to meet the original deadline. C — This is the correct option, as explained above. D — Completing the second half in *more* time than initially planned (which was 1.5 hours) would mean the total journey time would be even longer, failing to meet the original target. To compensate for the delay, the second half must be completed in *less* time (1 hour instead of 1.5 hours) than initially planned for that segment.

Calculate the distance Aidan covers before Ben starts. Aidan's speed = 4 km/h. Time Aidan walks before Ben starts = 30 minutes = 0.5 hours. Distance covered by Aidan = Speed × Time = 4 km/h × 0.5 h = 2 km. This 2 km is the head start distance Ben needs to cover. Calculate Ben's speed relative to Aidan. Ben's speed = 6 km/h, Aidan's speed = 4 km/h. Since they are moving in the same direction, Relative speed = Ben's speed - Aidan's speed = 6 km/h - 4 km/h = 2 km/h. Calculate the time it takes for Ben to cover the head start distance using the relative speed. Time = Distance / Relative speed = 2 km / 2 km/h = 1 hour. Convert 1 hour to minutes: 1 hour = 60 minutes. Why others are wrong: A — This is Aidan's initial head start time, not the time for Ben to catch up. B — Result of an incorrect calculation, possibly miscalculating the head start distance or relative speed. D — Result of an incorrect calculation, perhaps misinterpreting the relative movement or summing incorrect time values.

1. Calculate the train's normal scheduled speed: 240 km / 4 hours = 60 km/h. 2. Calculate the time taken to cover the first 120 km at the normal speed: 120 km / 60 km/h = 2 hours. 3. Determine the remaining distance to be covered: 240 km - 120 km = 120 km. 4. Calculate the time originally allocated for the remaining 120 km: 4 hours (total scheduled time) - 2 hours (time already spent) = 2 hours. 5. Account for the 30-minute delay: The train has 30 minutes (0.5 hours) less time to cover the remaining distance. So, the new available time is 2 hours - 0.5 hours = 1.5 hours. 6. Calculate the required speed for the remaining 120 km to arrive on time: 120 km / 1.5 hours = 80 km/h. Why others are wrong: A — 70 km/h would result in the train arriving late, as 120 km / 70 km/h ≈ 1.71 hours, which is more than the allowed 1.5 hours. B — 75 km/h would result in the train arriving late, as 120 km / 75 km/h = 1.6 hours, which is more than the allowed 1.5 hours. D — 90 km/h would result in the train arriving early, as 120 km / 90 km/h ≈ 1.33 hours, which is less than the required 1.5 hours. The question asks for the speed to ensure it arrives on time, implying the exact speed needed.

1. Calculate the total distance traveled: Total Distance = 120 km + 180 km = 300 km. 2. Calculate the time taken for the first part of the journey: Time1 = Distance1 / Speed1 = 120 km / 60 km/h = 2 hours. 3. Calculate the time taken for the second part of the journey: Time2 = Distance2 / Speed2 = 180 km / 90 km/h = 2 hours. 4. Calculate the total time taken for the entire journey: Total Time = Time1 + Time2 = 2 hours + 2 hours = 4 hours. 5. Calculate the average speed for the entire journey: Average Speed = Total Distance / Total Time = 300 km / 4 hours = 75 km/h. Why others are wrong: A — This value is likely a result of an arbitrary calculation error. B — This would be the average speed if the car traveled equal *distances* at the two given speeds (harmonic mean, 2*S1*S2/(S1+S2)). D — This value is a plausible but incorrect result, potentially from an error in summing distances or times, or an incorrect averaging method.

1. Calculate the distance Car P covers before Car Q starts: Distance = Speed × Time = 60 km/h × 2 h = 120 km. 2. This 120 km is the head start Car P has when Car Q begins its journey. 3. Determine the relative speed at which Car Q closes the distance on Car P. Since they are travelling in the same direction, Relative Speed = Speed of Car Q - Speed of Car P = 80 km/h - 60 km/h = 20 km/h. 4. Calculate the time it takes for Car Q to cover the 120 km head start at the relative speed: Time = Distance / Relative Speed = 120 km / 20 km/h = 6 hours. Why others are wrong: A — Incorrectly assumes a different initial distance for Car P's lead (e.g., 60 km) or an incorrect relative speed. B — Incorrectly assumes a different initial distance for Car P's lead (e.g., 80 km) or an incorrect relative speed. D — Likely results from an arithmetic error in calculating the initial distance or relative speed, or incorrectly adding Car P's initial travel time to the overtaking time.