Shortcut Trick
Speed1 = 75 mph; Time1 = 3 hr
Speed2 = 75 × 130% = 97.5 mph; Time2 = 2 hr
Average Speed = (v1t1 + v2t2) / (t1 + t2)
Average Speed = (75 × 3 + 97.5 × 2) / (3 + 2) = (225 + 195) / 5 = 420 / 5 = 84 mph.
∴ The correct answer is 84 miles per hr.
Alternate Method
Given:
Distance X-Y: Time = 3 hr, Speed = 75 mph
Distance Y-Z: Time = 2 hr, Speed = 30% increase over 75 mph
Formula: Average Speed = Total Distance ÷ Total Time
⇒ Distance (X to Y) = Speed × Time = 75 × 3 = 225 miles
⇒ Speed (Y to Z) = 75 + (30 ÷ 100 × 75) = 75 + 22.5 = 97.5 mph
⇒ Distance (Y to Z) = Speed × Time = 97.5 × 2 = 195 miles
⇒ Total Distance = 225 + 195 = 420 miles
⇒ Total Time = 3 + 2 = 5 hr
⇒ Average Speed = 420 ÷ 5 = 84 mph
∴ The correct answer is 84 miles per hr.
Additional Information
General Average Speed
The general formula for average speed is (Total Distance Covered) ÷ (Total Time Taken). It is the weighted average of speeds with respect to time.
Equal Distances Case
When a person travels two equal distances at speeds v1 and v2, the average speed is given by the harmonic mean: 2v1v2 ÷ (v1 + v2).
Equal Time Intervals Case
If a person travels at different speeds for equal time intervals, the average speed is the arithmetic mean of the speeds: (v1 + v2) ÷ 2.
Relative Speed
For two objects moving in the same direction, Relative Speed = v1 − v2. For opposite directions, Relative Speed = v1 + v2.