a bus driver took 120 minutes to travel from town X to town Y his average speed for the whole journey was 80km/h for the first 1/4 of the journey he drove an avg speed of 50km/h find his average speed
for the remaining 3/4 of the journey.
Let's first find the total distance traveled during the trip. We can do this by using the average speed for the whole journey and the total time taken.
Distance = Average_Speed * Time
Distance = 80km/h * 120min * (1h/60min)
Distance = 80km/h * 2h
Distance = 160km
Now we know that the driver traveled 160km during the trip. Out of this, he traveled 1/4th of the distance at an average speed of 50km/h.
1/4th_of_distance = (1/4) * 160km
1/4th_of_distance = 40km
Now we can find the total time taken for this first 1/4th distance using the speed-timedistance formula:
Time_for_1/4_distance = Distance_Speed/Average_Speed
Time_for_1/4_distance = 40km/50km/h
Time_for_1/4_distance = 0.8h
This would mean that the driver spent 0.8h or 48 minutes driving the first 1/4th of the distance.
Now we can find the time taken for the remaining 3/4th of the distance:
Total_time = 120minutes
Time_for_3/4_distance = Total_time - Time_for_1/4_distance
Time_for_3/4_distance = 72 minutes (120 - 48)
Now we can find the remaining 3/4th distance, which he traveled during the rest of the time:
3/4th_distance = Total_distance - 1/4th_distance
3/4th_distance = 160 km - 40 km
3/4th_distance = 120 km
Finally, we can find the average speed during the remaining 3/4th of the journey using the speed-timedistance formula:
Average_Speed = 3/4th_distance/Time_for_3/4_distance
Average_Speed = 120km / 72min * (1h/60min)
Average_Speed = 120km / 1.2h
Average_Speed = 100 km/h
Hence, the bus driver's average speed for the remaining 3/4 of the journey was 100 km/h.