Rohit travelled 1⅛ km from home to school, 5/6 km from school to skating rink,…
2022
Rohit travelled 1⅛ km from home to school, 5/6 km from school to skating rink, 2/3 km from skating rink to work and 1/4 km from work to home in 4 hours, 3 hours, 2 hours and 1 hour, respectively. Then the average speed of Rohit is
- A.
23/10 km/hour
- B.
23/8 km/hour
- C.
23/80 km/hour
- D.
20/80 km/hour
Attempted by 1 students.
Show answer & explanation
Correct answer: C
CONCEPT: Average speed for a journey made up of several legs is the TOTAL distance covered divided by the TOTAL time taken — it is NOT the average of the individual leg speeds.
APPLICATION:
Convert the mixed number to an improper fraction: 1⅛ km = 9/8 km.
Write every leg's distance over the common denominator 24 (the LCM of 8, 6, 3 and 4): 9/8 = 27/24 km, 5/6 = 20/24 km, 2/3 = 16/24 km, 1/4 = 6/24 km.
Add the four distances: total distance = (27 + 20 + 16 + 6)/24 = 69/24 = 23/8 km.
Add the four times: total time = 4 + 3 + 2 + 1 = 10 hours.
Average speed = total distance / total time = (23/8) / 10 = 23/80 km/hour.
CROSS-CHECK: Multiplying 23/80 km/hour back by the total time of 10 hours gives 23/8 km, which matches the independently-computed total distance, confirming the result.