A person travels three equal distances at speeds of 2 km/h, 3 km/h, and 4 km/h and takes a total time of 52 minutes. The total distance is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 2.4 km.
Distance = Speed × Time
Average speed = Total distance/Total time
Let the total distance traveled be 3X
Then every distance of X will be simultaneously covered with 2 km/hr, 3 km/hr, and 4 km/hr
Total time = 52 minutes, or 52/60 hrs
Total time required for traveling 3X km = X/2 + X/3 + X/4
⇒ X/2 + X/3 + X/4 = 52/60
⇒ 13X/12 = 52/60
⇒ X = 52/60 × 12/13
⇒ X = 4/5
Total distance = 3X = 3 × 4/5 = 12/5 = 4.5
The total distance is 2.4 km