Ravish travelled the first 20 km of an entire distance at a speed of 12 km/h; the next 25 km at a speed of 10 km/h and the remaining distance at a speed of 15 km/h. If his overall average speed was 13.5 km/h, what was the distance that Ravish travelled at a speed of 15 km/h?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 112.5 km
Given that
The first 20 km distance covered at a speed of 12 km/h.
The next 25 km distance was covered at a speed of 10 km/h.
The remaining distance (D) was covered at a speed of 15 km/h.
The average speed was 13.5 km/h
Formula used
The average speed = Total distance covered/Total time taken
Time = Distance/Speed
Calculations
⇒ 13.5 = (20 + 25 + D)/[(20/12) + (25/10) + (D/15)]
⇒ 13.5 = (45 + D)/[{(20 × 15) + (25 × 18) + (D × 12)}/180]
⇒ 13.5 = [180 × (45 + D)]/(300 + 450 + 12D)
⇒ 13.5 × (750 + 12D) = 8100 + 180D
⇒ 10125 + 162D = 8100 + 180D
⇒ 180D - 162D = 10125 - 8100
⇒ 18D = 2025
⇒ D = 112.5 km